U.S. patent number 8,405,890 [Application Number 12/524,725] was granted by the patent office on 2013-03-26 for system, apparatus and method for extracting image cross-sections of an object from received electromagnetic radiation.
This patent grant is currently assigned to CellOptic, Inc.. The grantee listed for this patent is Joseph Rosen. Invention is credited to Joseph Rosen.
United States Patent |
8,405,890 |
Rosen |
March 26, 2013 |
System, apparatus and method for extracting image cross-sections of
an object from received electromagnetic radiation
Abstract
An Apparatus and method to produce a hologram of a cross-section
of an object includes an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation, such as
light, from the object. The electromagnetic radiation assembly is
further configured to diffract the received electromagnetic
radiation and transmit a diffracted electromagnetic radiation An
image capture assembly is configure to capture an image of the
diffracted electromagnetic radiation and produce the hologram of
the cross-section of the object from the captured image. The
hologram of the cross-section includes information regarding a
single cross-section of the object.
Inventors: |
Rosen; Joseph (Omer,
IL) |
Applicant: |
Name |
City |
State |
Country |
Type |
Rosen; Joseph |
Omer |
N/A |
IL |
|
|
Assignee: |
CellOptic, Inc. (Rockville,
MD)
|
Family
ID: |
39674332 |
Appl.
No.: |
12/524,725 |
Filed: |
January 29, 2007 |
PCT
Filed: |
January 29, 2007 |
PCT No.: |
PCT/US2007/002448 |
371(c)(1),(2),(4) Date: |
July 28, 2009 |
PCT
Pub. No.: |
WO2008/094141 |
PCT
Pub. Date: |
August 07, 2008 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20100060962 A1 |
Mar 11, 2010 |
|
Current U.S.
Class: |
359/9; 359/29;
359/35 |
Current CPC
Class: |
G03H
1/08 (20130101); G03H 1/26 (20130101); G03H
5/00 (20130101); G03H 1/06 (20130101); G03H
1/0005 (20130101); G03H 1/041 (20130101); G03H
1/0443 (20130101); G03H 2226/11 (20130101); G03H
2223/23 (20130101); G03H 2210/33 (20130101); G03H
2001/0452 (20130101); G03H 2001/0033 (20130101) |
Current International
Class: |
G03H
1/08 (20060101); G03H 1/16 (20060101); G03H
1/04 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Other References
US. Appl. No. 12/374,139, filed Apr. 1, 2009, Rosen, et al. cited
by applicant .
U.S. Appl. No. 12/515,343, filed May 18, 2009, Rosen, et al. cited
by applicant .
U.S. Appl. No. 13/448,032, filed Apr. 16, 2012, Rosen, et al. cited
by applicant.
|
Primary Examiner: Chwasz; Jade R
Attorney, Agent or Firm: Oblon, Spivak, McClelland, Maier
& Neustadt, L.L.P.
Claims
The invention claimed is:
1. An apparatus configured to produce a hologram of a cross-section
of an object, said apparatus comprising: an electromagnetic
radiation assembly configured to receive a received electromagnetic
radiation from the object and transmit a transmitted
electromagnetic radiation based on the received electromagnetic
radiation, the transmitted electromagnetic radiation including the
hologram of the object; and an image capture assembly configured to
capture an image of the transmitted electromagnetic radiation and
produce the hologram of the cross-section of the object from the
captured image, the hologram of the cross-section including
information regarding a single cross-section of the object, wherein
the electromagnetic radiation apparatus includes a diffractive
electromagnetic radiation element or two lenses configured to
produce an off-axis Fresnel Zone pattern when the two lenses are
illuminated by a coherent light. wherein the electromagnetic
radiation apparatus includes a diffractive electromagnetic
radiation element or two lenses configured to produce an off-axis
Fresnel Zone pattern when the two lenses are illuminated by a
coherent light.
2. The apparatus of claim 1, wherein the electromagnetic radiation
apparatus includes only one radiation propagation axis and is
configured to propagate electromagnetic radiation only along the
radiation propagation axis in only one direction.
3. The apparatus of claim 1, wherein the electromagnetic radiation
assembly includes plural electromagnetic radiation elements each
having an axis of symmetry arranged along a same straight line.
4. The apparatus of claim 1, wherein the electromagnetic radiation
received from the object and the electromagnetic radiation
transmitted by the electromagnetic radiation assembly have a same
radiation propagation axis.
5. The apparatus of claim 1, wherein the hologram of the
cross-section includes a Fresnel hologram.
6. The apparatus of claim 1, wherein the electromagnetic radiation
assembly is configured to transmit the electromagnetic radiation
including a convolution of the received electromagnetic radiation
and a complex transmission function including a linear summation of
a first transformed pattern, a second transformed pattern and a
third transformed pattern, the first transformed pattern including
a first shifted concentric ring pattern, the second transformed
pattern including a second shifted concentric ring pattern, and the
third transformed pattern including a third shifted concentric ring
pattern.
7. The apparatus of claim 6, wherein each of the first, second and
third shifted concentric ring patterns includes a Fresnel Zone
Pattern or a portion of a Fresnel Zone Pattern.
8. The apparatus of claim 1, wherein a predetermined thickness and
coefficients of absorption or reflectance of the electromagnetic
radiation assembly is configured to control the phase and intensity
of the transmitted electromagnetic radiation.
9. The apparatus of claim 1, wherein the electromagnetic radiation
assembly further comprises: a first electromagnetic radiation
assembly configured to receive the received electromagnetic
radiation from the object and transmit a first transformed
electromagnetic radiation; a complex mask assembly configured to
receive the first transformed electromagnetic radiation from the
first electromagnetic radiation assembly, and transmit a complex
masked electromagnetic radiation according to a complex
transmission function; and a second electromagnetic radiation
assembly configured to receive the complex masked electromagnetic
radiation from the mask assembly, and transmit a second transformed
electromagnetic radiation as the diffracted electromagnetic
radiation.
10. The apparatus of claim 9, wherein the complex mask assembly
further comprises: a mask controller configured to vary the complex
transmission function of the electromagnetic radiation assembly
over time, said mask controller configured to vary the complex
transmission function to be based on a Fourier transform of a first
Fresnel Zone Pattern at a first time, a Fourier transform of a
second Fresnel Zone Pattern at a second time, and a Fourier
transform of a third Fresnel Zone Pattern at a third time.
11. The apparatus of claim 10, wherein the image capture assembly
further comprises: a timing controller configured to capture a
first partial image at the first time, a second partial image at
the second time, and a third partial image at the third time; and a
summing unit configured to produce the hologram of the
cross-section as a sum of the first partial image captured at the
first time, the second partial image captured at the second time,
and the third partial image captured at the third time.
12. The apparatus of claim 9, further comprising: an
electromagnetic radiation separating assembly configured to
separate the electromagnetic radiation received from the object
into three object electromagnetic radiation portions each including
a different frequency range; said first electromagnetic radiation
assembly including three first electromagnetic radiation
subassemblies each configured to receive one of the three object
electromagnetic radiation portions, and respectively transmit
first, second and third portions of the first transformed
electromagnetic radiation; said mask assembly including first,
second and third mask subassemblies respectively configured to
receive the first, second and third portions of the first
transformed electromagnetic radiation, and respectively transmit
first, second and third complex mask transformed electromagnetic
radiation; and said second electromagnetic radiation assembly
including three second electromagnetic radiation subassemblies
respectively configured to receive first, second and third complex
mask transformed electromagnetic radiation, and respectively
transmit first, second and third portions of transmitted
electromagnetic radiation.
13. The apparatus of claim 12, wherein the first mask subassembly
is configured to transmit the first complex mask transformed
electromagnetic radiation based on a Fourier transform of a first
Fresnel Zone Pattern, the second mask subassembly is configured to
transmit the second complex mask transformed electromagnetic
radiation based on a Fourier transform of a second Fresnel Zone
Pattern, and the third mask subassembly is configured to transmit
the third complex mask transformed electromagnetic radiation based
on a Fourier transform of a third Fresnel Zone Pattern.
14. The apparatus of claim 1, further comprising: an objective
assembly arranged between the object and the electromagnetic
radiation assembly and configured to collimate, focus, invert or
modify the electromagnetic radiation from the object, prior to the
received electromagnetic radiation being received at the
electromagnetic radiation assembly.
15. The apparatus of claim 1, wherein the hologram of the
cross-section includes information regarding only the single
cross-section of the object.
16. The apparatus of claim 1, wherein the cross-section of the
object includes an observable portion of the object that exists on
a plane perpendicular to the direction of the received
electromagnetic radiation.
17. An apparatus configured to produce a hologram of a
cross-section of an object, said apparatus comprising: an
electromagnetic radiation assembly configured to receive a received
electromagnetic radiation from the object and transmit a
transmitted electromagnetic radiation based on the received
electromagnetic radiation, the transmitted electromagnetic
radiation including the hologram of the object; and an image
capture assembly configured to capture an image of the transmitted
electromagnetic radiation and produce the hologram of the
cross-section of the object from the captured image, the hologram
of the cross-section including information regarding a single
cross-section of the object, wherein the electromagnetic radiation
assembly further includes a first electromagnetic radiation
assembly configured to receive the received electromagnetic
radiation from the object and transmit a first transformed
electromagnetic radiation, a complex mask assembly configured to
receive the first transformed electromagnetic radiation from the
first electromagnetic radiation assembly, and transmit a complex
masked electromagnetic radiation according to a complex
transmission function, and a second electromagnetic radiation
assembly configured to receive the complex masked electromagnetic
radiation from the mask assembly, and transmit a second transformed
electromagnetic radiation as the diffracted electromagnetic
radiation.
18. An apparatus configured to produce a hologram of a
cross-section of an object, said apparatus comprising: an
electromagnetic radiation assembly configured to receive a received
electromagnetic radiation from the object and transmit a
transmitted electromagnetic radiation based on the received
electromagnetic radiation, the transmitted electromagnetic
radiation including the hologram of the object; an image capture
assembly configured to capture an image of the transmitted
electromagnetic radiation and produce the hologram of the
cross-section of the object from the captured image, the hologram
of the cross-section including information regarding a single
cross-section of the object; and an electromagnetic radiation
separating assembly configured to separate the electromagnetic
radiation received from the object into three object
electromagnetic radiation portions each including a different
frequency range; a first electromagnetic radiation assembly
including three first electromagnetic radiation subassemblies each
configured to receive one of the three object electromagnetic
radiation portions, and respectively transmit first, second and
third portions of a transformed electromagnetic radiation; a mask
assembly including first, second and third mask subassemblies
respectively configured to receive the first, second and third
portions of the transformed electromagnetic radiation, and
respectively transmit first, second and third complex mask
transformed electromagnetic radiation; and a second electromagnetic
radiation assembly including three second electromagnetic radiation
subassemblies respectively configured to receive first, second and
third complex mask transformed electromagnetic radiation, and
respectively transmit first, second and third portions of
transmitted electromagnetic radiation.
Description
CROSS-REFERENCE TO A RELATED APPLICATION
This application is related to International Patent Application No.
PCT/US2006/027727 filed Jul. 18, 2006, which is incorporated herein
by reference in its entirety.
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to an apparatus for capturing
electromagnetic radiation, such as light or other forms of
electromagnetic radiation, from an object and extracting object
geometric information from the received radiation, in the field of
three-dimensional imaging and holography. The invention also
relates to a system and method of performing those functions.
2. Discussion of the Background
Conventional techniques for capturing three-dimensional information
from physical objects include holography, range-finding, and
tomography. However, conventional techniques may disadvantageously
require an active illumination source, or place limitations on a
light source (e.g., may require coherent light, a point light
source or a bandwidth limited light), place limitations on movement
of the object or the sensing apparatus (e.g., require that the
object and sensing device be stationary, or require that they be
moved in a predetermined fashion), may require complex
electromagnetic radiation assemblies (e.g., complex arrangement of
mirrors and lenses), and may produce poor quality three-dimensional
images having low resolution or low fidelity.
SUMMARY OF THE INVENTION
Accordingly, one object of this invention is to provide an
apparatus configured to produce a hologram of a cross-section of an
object, said apparatus comprising: an electromagnetic radiation
assembly configured to receive a received electromagnetic radiation
from the object, diffract the received electromagnetic radiation,
and transmit a diffracted electromagnetic radiation; and an image
capture assembly configured to capture an image of the diffracted
electromagnetic radiation, and produce the cross-section of the
object from the captured image, the hologram is including
information regarding a single cross-section of the object.
Another object of this invention is to provide a novel apparatus,
wherein several holograms of the object's cross-sections are
captured and processed in serial or parallel way.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation includes light.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation apparatus includes only one
radiation propagation axis and is configured to propagate
electromagnetic radiation only along the radiation propagation axis
in only one direction.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly includes plural
electromagnetic radiation elements each having an axis of symmetry
arranged along a same straight line.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly includes plural
electromagnetic radiation elements each having a geometric center
arranged along a same straight line.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation received from the object and
the electromagnetic radiation diffracted by the electromagnetic
radiation assembly have a same radiation propagation axis.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation received from the object
includes incoherent light.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation received from the object is
produced by the object.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation received from the object does
not interfere with an electromagnetic radiation that is not
received from the object to produce the hologram of the
cross-section of the object.
Another object of this invention is to provide a novel apparatus,
wherein the object and the apparatus are configured to remain
stationary during the capture of the image.
Another object of this invention is to provide a novel apparatus,
wherein each portion of the electromagnetic apparatus is configured
to remain stationary during the capture of the image.
Another object of this invention is to provide a novel apparatus,
wherein at least one of the object or the apparatus is configured
to be in motion during the capture of the image.
Another object of this invention is to provide a novel apparatus,
wherein the hologram of the cross-section is produced from a single
captured image.
Another object of this invention is to provide a novel apparatus,
wherein the hologram of the cross-section is produced from plural
captured images.
Another object of this invention is to provide a novel apparatus,
wherein the hologram of the cross-section includes a Fresnel
hologram.
Another object of this invention is to provide a novel apparatus,
wherein the hologram of the cross-section includes a random phase
hologram.
Another object of this invention is to provide a novel apparatus,
wherein a phase and intensity of the diffracted electromagnetic
radiation is described by a convolution of the received
electromagnetic radiation from object's cross section and a Fresnel
Zone Plate.
Another object of this invention is to provide a novel apparatus,
wherein a phase and intensity of the diffracted electromagnetic
radiation is described by a convolution of the received
electromagnetic radiation from object's cross section and a random
phase function.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly is configured to
transmit the electromagnetic radiation including a convolution of
the received electromagnetic radiation and a complex transmission
function including a linear summation of a first transformed
pattern, a second transformed pattern and a third transformed
pattern, the first transformed pattern including a first shifted
concentric ring pattern, the second transformed pattern including a
second shifted concentric ring pattern, and the third transformed
pattern including a third shifted concentric ring pattern.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly is configured to
transmit the electromagnetic radiation including a convolution of
the received electromagnetic radiation and a complex transmission
function including a linear summation of a first transformed
pattern, and a second transformed pattern, the first transformed
pattern including a first shifted random pattern, and the second
transformed pattern including a second shifted random pattern.
Another object of this invention is to provide a novel apparatus,
wherein each of the first, second and third shifted concentric ring
patterns are shifted away from one another in a same plane of the
electromagnetic radiation assembly.
Another object of this invention is to provide a novel apparatus,
wherein each of the first, second and third shifted concentric ring
patterns includes a Fresnel Zone Pattern or a portion of a Fresnel
Zone Pattern.
Another object of this invention is to provide a novel apparatus,
wherein the portion of the Fresnel Zone Pattern includes a Fresnel
Zone Pattern having one or more rings removed, one or more extra
rings added, one or more rings having a varied width, or one or
more rings having a portion of the ring removed.
Another object of this invention is to provide a novel apparatus,
wherein a phase of the Fresnel Zone Pattern or the portion of the
Fresnel Zone Pattern in each of the first, second and third shifted
concentric ring pattern is different.
Another object of this invention is to provide a novel apparatus,
wherein a predetermined thickness and coefficients of absorption or
reflectance of the electromagnetic radiation assembly is configured
to control the phase and intensity of the diffracted light.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly is configured to
control at least one of the phase or intensity of the transmitted
electromagnetic radiation by varying a thickness of a material
through which electromagnetic radiation passes.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly further comprises: a
first electromagnetic radiation assembly configured to receive the
received electromagnetic radiation from the object and transmit a
first transformed electromagnetic radiation; a complex mask
assembly configured to receive the first transformed
electromagnetic radiation from the first electromagnetic radiation
assembly, and transmit a complex masked electromagnetic radiation
according to a complex transmission function; and a second
electromagnetic radiation assembly configured to receive the
complex masked electromagnetic radiation from the mask assembly,
and transmit a second transformed electromagnetic radiation as the
diffracted electromagnetic radiation.
Another object of this invention is to provide a novel apparatus,
wherein the complex mask assembly further comprises: a mask
controller configured to vary the complex transmission function of
the electromagnetic radiation assembly over time, said mask
controller configured to vary the complex transmission function to
be based on a Fourier transform of a first Fresnel Zone Pattern at
a first time, a Fourier transform of a second Fresnel Zone Pattern
at a second time, and a Fourier transform of a third Fresnel Zone
Pattern at a third time.
Another object of this invention is to provide a novel apparatus,
wherein the image capture assembly further comprises: a timing
controller configured to capture a first partial image at the first
time, a second partial image at the second time, and a third
partial image at the third time; and a summing unit configured to
produce the hologram of the cross-section as a sum of the first
partial image captured at the first time, the second partial image
captured at the second time, and the third partial image captured
at the third time.
Another object of this invention is to provide a novel apparatus,
further comprising: an electromagnetic radiation separating
assembly configured to separate the electromagnetic radiation
received from the object into three object electromagnetic
radiation portions each including a different frequency range; said
first electromagnetic radiation assembly including three first
electromagnetic radiation subassemblies each configured to receive
one of the three object electromagnetic radiation portions, and
respectively transmit first, second and third portions of the first
transformed electromagnetic radiation; said mask assembly including
first, second and third mask subassemblies respectively configured
to receive the first, second and third portions of the first
transformed electromagnetic radiation, and respectively transmit
first, second and third complex mask transformed electromagnetic
radiation; and said second electromagnetic radiation assembly
including three second electromagnetic radiation subassemblies
respectively configured to receive first, second and third complex
mask transformed electromagnetic radiation, and respectively
transmit first, second and third portions of transmitted
electromagnetic radiation.
Another object of this invention is to provide a novel apparatus,
wherein the first mask subassembly is configured to transmit the
first complex mask transformed electromagnetic radiation based on a
Fourier transform of a first Fresnel Zone Pattern, the second mask
subassembly is configured to transmit the second complex mask
transformed electromagnetic radiation based on a Fourier transform
of a second Fresnel Zone Pattern, and the third mask subassembly is
configured to transmit the third complex mask transformed
electromagnetic radiation based on a Fourier transform of a third
Fresnel Zone Pattern.
Another object of this invention is to provide a novel apparatus,
wherein the image capture assembly includes at least one of a CCD,
a CMOS light sensitive device, another electronic camera, a light
sensitive emulsion, or another photosensitive device.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly consists of i) one
diffractive electromagnetic radiation element and ii) one
converging lens or mirror.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly consists of i) one
diffractive electromagnetic radiation element and ii) two
converging lenses or two mirrors.
Another object of this invention is to provide a novel apparatus,
further comprising: an objective assembly arranged between the
object and the electromagnetic radiation assembly and configured to
collimate, focus, invert or modify the electromagnetic radiation
from the object, prior to the received electromagnetic radiation
being received at the electromagnetic radiation assembly.
Another object of this invention is to provide a novel apparatus,
wherein the objective assembly includes at least one of an
objective lens, a zoom lens, a macro lens, a microscope, a
telescope, a prism, a filter, a monochromatic filter, a dichroic
filter, a complex objective lens, a wide-angle lens, a camera, a
pin-hole, a light slit, or a mirror.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation' apparatus includes a
diffractive electromagnetic radiation element configured to produce
an off-axis Fresnel Zone pattern when the diffractive element is
illuminated by a coherent plane wave.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation includes at least one of an
x-ray radiation, a microwave radiation, an infrared light, a radio
frequency signal or an ultraviolet light.
Another object of this invention is to provide a novel apparatus,
wherein the electromagnetic radiation assembly and the image
capture assembly do not include any reflective electromagnetic
radiation elements.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object along a radiation axis in an electromagnetic radiation
receiving direction, transmit a transmitted electromagnetic
radiation along the radiation axis in the electromagnetic radiation
receiving direction, and interfere a first portion of the
transmitted electromagnetic radiation with a second portion of the
transmitted electromagnetic radiation the transmitted
electromagnetic radiation; and an image capture assembly configured
to capture an image of the transmitted electromagnetic radiation
transmitted along the optical axis in the electromagnetic radiation
receiving direction, and produce the hologram of the cross-section
of the object from the captured image, wherein the radiation axis
is a straight line, the hologram of the cross-section including
information regarding a single cross-section of the object.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object and transmit a transmitted electromagnetic radiation based
on the received electromagnetic radiation, the transmitted
electromagnetic radiation including the holograms of the object's
cross-sections; and an image capture assembly configured to capture
an image of the transmitted electromagnetic radiation and produce
the hologram of the cross-section from the captured image, the
hologram of the cross-section including information regarding a
single cross-section of the object.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, transmit a transmitted electromagnetic radiation based on
the received electromagnetic radiation, and interfere a first
portion of the transmitted electromagnetic radiation with a second
portion of the transmitted electromagnetic radiation; and an opaque
image capture assembly configured to capture an image of the
transmitted electromagnetic radiation produced by the interference
of at least the first and second portions of the transmitted
electromagnetic radiation, and produce the hologram of the
cross-section of the object from the captured image, wherein a
center of the electromagnetic radiation assembly and a center of
the image capture assembly are arranged along a same straight
line.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
consisting of one diffractive electromagnetic radiation element and
configured to receive a received electromagnetic radiation from the
object and transmit a transmitted electromagnetic radiation based
on the received electromagnetic radiation; and an image capture
assembly configured to capture an image of the transmitted
electromagnetic radiation, and produce the hologram of the
cross-section of the object from the captured image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, perform a transformation of the received electromagnetic
radiation, and transmit the transformed received electromagnetic
radiation, the transformation including a convolution of a function
representing an intensity distribution of the received
electromagnetic radiation and a concentric ring function; and an
image capture assembly configured to capture an image of the
transmitted electromagnetic radiation, and produce the hologram of
the object from the captured image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, perform a transformation of the received electromagnetic
radiation, and transmit the transformed received electromagnetic
radiation, the transformation including a convolution of i) an
intensity distribution of the received electromagnetic radiation
and ii) a function having regions of positive slope and negative
slope when evaluated between a center of the optical assembly and
an outer edge of the optical assembly; and an image capture
assembly configured to capture an image of the transmitted
electromagnetic radiation, and produce the hologram of the
cross-section of the object from the captured image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to convolve i) a received electromagnetic radiation
received from the object and ii) a curve having plural inflection
points between a center of the optical assembly and an edge of the
optical assembly, and transmit the convolved electromagnetic
radiation; and an image capture assembly configured to capture an
image of the convolved electromagnetic radiation, and produce the
hologram of the cross-section of the object from the captured
image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, perform a transformation of the received electromagnetic
radiation, and transmit the transformed received electromagnetic
radiation, the transformation including a convolution of i) an
intensity distribution of the received electromagnetic radiation
and ii) a transformation function that is a linear combination of
three partial transformation functions, each including a concentric
ring pattern; and an image capture assembly configured to capture
an image of the transmitted electromagnetic radiation, and produce
the hologram of the cross-section of the object from the captured
image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of a
chemiluminescent object, said apparatus comprising: an
electromagnetic radiation assembly configured to receive a received
chemiluminescent radiation from the object, and transmit a
transmitted electromagnetic radiation including the hologram of the
cross-section of the object; and an image capture assembly
configured to capture an image of the transmitted electromagnetic
radiation, and produce the hologram of the cross-section of the
object from the captured image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a scattered electromagnetic radiation
scattered by the object, which scatters a source electromagnetic
radiation, and transmit a transmitted electromagnetic radiation
based on the received scattered electromagnetic radiation, the
transmitted electromagnetic radiation being independent of any
source electromagnetic radiation that is not scattered by the
object; and an image capture assembly configured to capture an
image of the transmitted electromagnetic radiation and produce the
hologram of the cross-section of the object from the captured
image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to diffract an electromagnetic radiation received from
the object; and an image capture assembly configured to capture an
image of the diffracted electromagnetic radiation and produce the
hologram of the cross-section of the object from the captured
image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: plural electromagnetic radiation sources
configured to radiate the object with plural electromagnetic
radiation signals; an electromagnetic radiation assembly configured
to receive a received electromagnetic radiation from the object and
transform the received electromagnetic radiation, the received
electromagnetic radiation including portions of the plural source
electromagnetic radiation signals scattered by the object; and a
capture assembly configured to capture an image of the transformed
electromagnetic radiation and produce the hologram of the
cross-section of the object from the captured image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of a
fluorescent object, said apparatus comprising: an electromagnetic
radiation assembly configured to receive a received fluorescent
radiation from the object and transmit a transmitted
electromagnetic radiation based on the received fluorescent
radiation; and an image capture assembly configured to capture an
image of the transmitted electromagnetic radiation and produce the
hologram of the cross-section of the object from the captured
image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of a black body
radiation radiating object, said apparatus comprising: an
electromagnetic radiation assembly configured to receive a received
black body electromagnetic radiation from the object, and transmit
a transmitted electromagnetic radiation based on the received black
body electromagnetic radiation from the object; and an image
capture assembly configured to capture an image of the transmitted
electromagnetic radiation and produce the hologram of the
cross-section of the object from the captured image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, transmit a transmitted electromagnetic radiation based only
on the received electromagnetic radiation from the object, and
interfere a first portion of the transmitted electromagnetic
radiation with a second portion of the transmitted electromagnetic
radiation; and an image capture assembly configured to capture a
fringe pattern produced by the interference of at least the first
and second portions of the transmitted electromagnetic radiation
and produce the hologram of the cross-section of the object from
the fringe pattern.
Another object of this invention is to provide a novel
electromagnetic radiation apparatus configured to produce a
hologram of a cross-section of an object, said apparatus configured
to receive a received electromagnetic radiation from the object,
diffract the received electromagnetic radiation, and transmit a
diffracted electromagnetic radiation including the hologram of the
cross-section of the object.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of a scene,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
scene, diffract the received electromagnetic radiation, and
transmit a diffracted electromagnetic radiation; and an image
capture assembly configured to capture an image of the diffracted
electromagnetic radiation, and produce the hologram of the
cross-section of the scene from the captured image.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object, transform the received electromagnetic radiation, and
transmit the transformed electromagnetic radiation including a
fringe pattern; and an image capture assembly configured to capture
an image of the fringe pattern and produce the hologram of the
cross-section of the object from the captured fringe pattern.
Another object of this invention is to provide a novel apparatus
configured to produce a hologram of a cross-section of an object,
said apparatus comprising: an electromagnetic radiation assembly
configured to receive a received electromagnetic radiation from the
object and transform the received electromagnetic radiation; and an
image capture assembly configured to capture the transformed
electromagnetic radiation including the hologram of the
cross-section of the object, said holograms includes fringe
patterns produced by an interference of the received
electromagnetic radiation with itself, and said holograms not
including fringe patterns produced by an interference of the
received electromagnetic radiation with any other electromagnetic
radiation.
Another object of this invention is to provide a novel method for
producing a hologram of a cross-section of an object, said method
comprising steps of: receiving a received electromagnetic radiation
from the object; transmitting a diffracted electromagnetic
radiation based on the received electromagnetic radiation;
capturing an image of the diffracted electromagnetic radiation; and
producing the hologram of the cross-section of the object from the
captured image.
Another object of this invention is to provide a novel apparatus,
wherein the received electromagnetic radiation does not include
coherent light.
Another object of this invention is to provide a novel apparatus,
wherein the hologram of the cross-section includes information
regarding only the single cross-section of the object.
Another object of this invention is to provide a novel apparatus,
wherein the cross-section of the object includes an observable
portion of the object that exists on a plane perpendicular to the
direction of the received electromagnetic radiation.
BRIEF DESCRIPTION OF THE DRAWINGS
A more complete appreciation of the invention and many of the
attendant advantages thereof will be readily obtained as the same
becomes better understood by reference to the following detailed
description when considered in connection with the accompanying
drawings, wherein:
FIG. 1 is a block diagram of an optical apparatus according to an
embodiment of the present invention;
FIG. 2 is a block diagram that illustrates an example of captured
geometric information according to embodiments of the present
invention;
FIG. 3 is a block diagram of an incoherent correlator that may be
used as the optical assembly in the optical apparatus of FIG.
1;
FIG. 4 is a block diagram of an embodiment of an optical apparatus
that includes an optical assembly;
FIG. 5 is a detailed front view of another embodiment of a mask
that includes a diffractive optical element (DOE) having an array
of plural transform regions;
FIG. 6 is an example of a binary Fresnel Zone Pattern;
FIG. 7A is an example of a sinusoidal FZP;
FIG. 7B is an example of another sinusoidal FZP;
FIG. 7C is an example of another sinusoidal FZP;
FIG. 8A is an example of a phase distribution of a Fourier
Transformed FZP pattern with random phase distribution;
FIG. 8B is another example of a phase distribution of a Fourier
Transformed FZP pattern with random phase distribution;
FIG. 8C is another example of a phase distribution of a Fourier
Transformed FZP pattern with random phase distribution;
FIG. 9A is the amplitude portion of a complex transmission function
that is a Fourier Transform of a linear combination of three FZP
functions each having random phase distributions;
FIG. 9B is the phase portion of a complex transmission function
that is a Fourier Transform of a linear combination of three FZP
functions each having random phase distributions;
FIG. 9C is an example of a pattern on a CCD when a point object is
present at the input;
FIG. 10A is a block diagram of an embodiment of an image capture
assembly;
FIG. 10B is a block diagram of another embodiment of an image
capture assembly;
FIG. 11A is a view of an embodiment of a light intensity capture
device that includes a charge coupled device having three distinct
regions;
FIG. 11B is an example of a two-dimensional intensity image
including three partial holograms;
FIG. 12A is an example of an arrangement of distinct regions in an
embodiment of a light capturing device;
FIG. 12B is another example of an arrangement of distinct regions
in an embodiment of a light capturing device;
FIG. 12C is another example of an arrangement of distinct regions
an embodiment of a light capturing device;
FIG. 13 is a block diagram of an embodiment of a capture control
unit that includes an image data processor that combines the
electronic image data;
FIG. 14 is a block diagram of an embodiment of an optical apparatus
that varies the mask over time;
FIG. 15 is a block diagram of a controllable mask that includes a
spatial light modulator under the control of a mask controller;
FIG. 16 is a block diagram of another embodiment of an optical
apparatus in which the mask is varied over time;
FIG. 17 is a block diagram of another embodiment of an optical
apparatus;
FIG. 18 is a block diagram of another embodiment of an optical
apparatus;
FIG. 19 is a block diagram of another embodiment of an optical
apparatus;
FIG. 20A is a block diagram of an example of an optical apparatus
that does not require a second transforming optical element;
FIG. 20B is a block diagram of an example of an optical apparatus
that does not require a first transforming optical element;
FIG. 20C is a block diagram of an example of an optical apparatus
that does not require first and second transforming optical
elements;
FIG. 21 is a block diagram of an embodiment of an optical apparatus
including a reflective type diffractive optical element;
FIG. 22A is a block diagram of another embodiment of an optical
apparatus;
FIG. 22B is a block diagram of another embodiment of an optical
apparatus;
FIG. 23 is a block diagram of another embodiment of an optical
apparatus;
FIG. 24 is an example of an off-axis Fresnel Zone Pattern;
FIG. 25 is a block diagram of a portion of an optical apparatus
including a composite mask;
FIG. 26 is a block diagram of a method for calculating a
filter;
FIG. 27A is a block diagram of another embodiment of an optical
apparatus;
FIG. 27B is a block diagram of another embodiment of an optical
apparatus;
FIG. 27C is a block diagram of another embodiment of an optical
apparatus;
FIG. 27D is a block diagram of another embodiment of an optical
apparatus;
FIG. 28A is a block diagram of another embodiment of an optical
apparatus;
FIG. 28B is a block diagram of another embodiment of an optical
apparatus;
FIG. 28C is a block diagram of another embodiment of an optical
apparatus;
FIG. 28D is a block diagram of another embodiment of an optical
apparatus;
FIG. 29 is a block diagram of another embodiment of an optical
apparatus;
FIG. 30A is a block diagram of another embodiment of an optical
apparatus;
FIG. 30B is a block diagram of another embodiment of an optical
apparatus;
FIG. 30C is a block diagram of another embodiment of an optical
apparatus;
FIG. 30D is a block diagram of another embodiment of an optical
apparatus;
FIG. 31 is a block diagram of a conventional holographic
system.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Conventional holographic techniques may include methods of
capturing a hologram of an object by capturing an interference
pattern that results when a first portion of a coherent laser light
beam (e.g., reference beam) interferes with a second portion of the
laser light beam reflected off the object (e.g., object beam). A
three-dimensional image of the object may be viewed by
appropriately illuminating the recorded interference pattern with
the reference beam.
FIG. 31 is a block diagram of a conventional holographic system
including a laser 9000 that shines a coherent laser light beam
along a first optical axis 9026 through a partially reflective and
transmissive mirror, such as a beam splitter 9002. A first portion
of the split laser beam is guided by lens 9004 and mirror 9008 to
illuminate the object 9014 with the object beam 9010 along a second
optical axis 9024. A second portion of the split laser beam is
reflected by the beamsplitter 9002 along a third optical axis 9018
and guided by lens 9006 and mirror 9028 to direct a reference beam
9012 along a fourth optical axis 9020 to an image capture device
9016 such as a photographic plate, a charge coupled device (CCD) or
a complementary metal oxide semiconductor sensor (CMOS). The
reference beam 9012 and the object beam 9010 reflected from the
object 9014 along a fifth optical axis 9022 interfere with each
other, producing an interference pattern that may be recorded as a
hologram on the image capture device 9016.
Conventional holography solutions that produce a hologram by
interfering two parts of a light source along different optical
paths or optical axes may be very sensitive to any change in
alignment of the optical paths or axes, because even minor changes
in the length or direction of the optical paths or axes will change
the phase relationship of the portions of light that interfere.
Such a change will result in a change to the resulting interference
pattern and hologram, and yield a distorted resulting image.
For example, in the holography system of FIG. 31, a factor such as
motion, vibration, component deterioration or distortion, or
thermal expansion, may cause a slight change in the length or
direction of one or more of the first, second, third, fourth or
fifth optical axes 9026, 9024, 9018, 9020 and 9022, respectively.
Even a slight change in one of the axes may cause a corresponding
change in the phase relationship of the reference beam 9012 and the
light reflected from the object 9014 along the fifth optical axis
9010, thereby causing a significant change in the resulting
interference pattern and hologram captured at the image capture
device 9016.
Such a sensitivity to axial variation in conventional holographic
systems may result in reduced resolution in the resulting
three-dimensional information.
Various conventional attempts to address such a sensitivity to
axial variation have had limited success. For example, attempts
have included using massive platforms and shock absorbers to dampen
vibration, high tolerance mechanical optical stages to reduce
positioning errors, and optical and structural materials having
reduced coefficients of thermal expansion to reduce thermal
expansion effects. However, these attempts generally increase the
cost, size and mass of conventional holography systems, and reduce
system portability and availability.
In addition, conventional holography systems may require an active
light source to illuminate the object and produce the reference and
object beams. Active solutions that require illumination of the
object by a particular light source may limit the applicability and
usefulness of the conventional holography systems. For example, an
active light source would not be useful in stealth military
targeting holographic systems where it would be undesirable for the
targeting device to give away its position by producing light or
other electromagnetic radiation. Alternatively, an active radiation
source would not be applicable in holographic systems that observe
objects that produce their own light, such as a holographic system
observing chemiluminescent, black body, or infrared illuminating
objects. Such a holographic technique may be useful in observing
objects such as ships by virtue of their ability to block the
chemiluminescence of background emissions in certain bodies of
water, such as the chemiluminescent Red Sea.
In addition, conventional holographic systems that rely on a
coherent light source, such as a monochromatic laser, may be unable
to capture color information from the object unless multi-line
lasers or multiple lasers of different wavelengths are used.
Systems such as those are likely to be very complex. Further, such
systems may not be suitable for capturing three-dimensional
information regarding objects that should not be illuminated with
laser light (e.g., sensitive biological material).
Conventional holographic techniques using incoherent light to
illuminate an object rely on a simplifying assumption that
incoherent source objects may be considered to be composed of many
individual light source points, each of which is self coherent, and
each of which can therefore create an interference pattern with its
mirrored image. For the purposes of this document, incoherent light
is any temporally or spatially incoherent light for which any two
electromagnetic fields emitted from a same location at two
different times (in the case of temporal incoherence) or emitted
from two different locations at the same time (in the case of
spatial incoherence) do not create an interference grating or
pattern when the two fields are summed together. Various methods of
incoherent holography have been proposed using this principle, such
as methods described in A. W. Lohmann, "Wavefront Reconstruction
for Incoherent Objects," J. Opt. Soc. Am. 55, 1555-1556 (1964), G.
Cochran, "New method of making Fresnel transforms," J. Opt. Soc.
Am. 56, 1513-1517 (1966), P. J. Peters, "Incoherent holography with
mercury light source," Appl. Phys. Lett. 8, 209-210 (1966), H. R.
Worthington, Jr., "Production of holograms with incoherent
illumination," J. Opt. Soc. Am. 56, 1397-1398 (1966), A. S.
Marathay, "Noncoherent-object hologram: its reconstruction and
optical processing," J. Opt. Soc. Am. A 4, 1861-1868 (1987), and G.
Sirat, D. Psaltis, "Conoscopic holography," Optics Letters, 10, 4-6
(1985), each of which is incorporated herein by reference.
However, the conventional incoherent holographic techniques may
require impractically high levels of light intensity. Thus,
conventional incoherent holographic systems require active
illumination of objects, and therefore may exhibit the resulting
problems and limitations described above.
In addition, conventional incoherent holographic systems may rely
on illuminating the object with a bandwidth limited source to
reduce sensitivity to length differences in the plural optical path
differences. For example, in a conventional incoherent holographic
system acceptable variations in the relative length of optical
paths may be limited to the inverse of the bandwidth multiplied by
the light velocity. Thus, a predetermined light source having a
limited bandwidth may be required, and the elimination of
extraneous illumination may be necessary in conventional incoherent
holographic systems.
Further, conventional incoherent holographic systems may require
optical arrangements having plural optical axes similar to the
example shown in FIG. 31. Thus, conventional incoherent holographic
systems may also be susceptible to variations in direction or
length of the optical axes, and attendant problems, as described
above.
In addition, conventional holographic techniques involve splitting
light into two channels using mirrors, which may have a low
transfer efficiency, and then recombining the split light. The
efficiency may be particularly low in the recombination where more
than 50% of the power gets lost.
Further, in a conventional Fourier hologram, each object point is
transformed to a linear grating throughout the entire image plane
(e.g., throughout an entire CCD plane). Thus, in conventional
incoherent methods of producing Fourier holograms, light from each
object point must disadvantageously be intense enough to establish
a high contrast grating or pattern over the entire image plane.
In addition, when viewed by human eyes, a conventional hologram may
create an authentic illusion of viewing a realistic 3D scene.
However, reconstructing the same hologram by a computer creates a
virtual 3D space in which it may be difficult to know where exactly
the image is in-focus, and what is the exact distance of each
object from the camera. A conventional hologram may include only a
2D matrix and thus may not adequately represent all of the
information contained in the 3D scene.
Tomographic methods have been proposed to overcome the limitations
of conventional holographic techniques described above. Such
tomographic methods may involve capturing plural images of an
object from different points of view, for example by moving the
object, or the camera, or both, in between successive images, and
extracting three-dimensional object information by processing the
successive images. Conventional tomographic methods are described
in Y. Li, D. Abookasis and J. Rosen, "Computer-generated holograms
of three-dimensional realistic objects recorded without wave
interference," Appl. Opt. 40, 2864-2870 (2001), and Y. Sando, M.
Itoh, and T. Yatagai, "Holographic three-dimensional display
synthesized from three-dimensional Fourier spectra of real existing
objects," Opt. Lett 28, 2518-2520 (2003), each of which is
incorporated herein by reference.
Tomographic methods may be slow, however, as they may require
plural images to be captured before and after a relative
perspective between the object and camera is changed and thus may
not be able to capture objects which change during the time it
takes to capture the multiple images. Alternatively, tomographic
methods may require more expensive or physically large equipment
that includes the ability to simultaneously capture images of the
object from more than one perspective. Further, the methods may be
impractical for distant objects or immovable objects for which it
may be difficult to change a relative perspective from the camera.
In addition, if the object is moving in an unpredictable way, it
may be difficult to extract information from successive images
without having another source of information regarding the shape or
the movements of the object.
Range-finding methods involve measuring the distance between an
apparatus and various points on a surface of an object, and
constructing an image or model of the object based on the
distances. Further, some range-finding methods may include a
predetermined or controlled movement of the object or the apparatus
to predictably change the view of the object from the apparatus
over time. Thus, the conventional range-finding methods may also
include the predictable change in the view of the object to
determine an exterior three-dimensional shape of the object.
Conventional range-finding methods include systems that illuminate
points on an object with a laser, and measuring the amount of time
required for the laser light to travel between the object and the
laser source to determine a distance to the object based on the
travel time. Related methods include "painting" an object with a
laser stripe or grid and examining a deformation in the observed
grid to determine geometric information of the object.
However, such range-finding methods require active illumination of
the object by a coherent laser, and therefore are not suitable for
incoherently illuminated objects or for fluorescent or luminescent
emitting objects. When coherent light sources can be used, they
have the attendant problems and limitations of active illumination
and coherent light sources described above. Further, the methods
may be difficult to perform if the object is moving in an
unpredictable way, or if the object is very close to the laser
source.
Other range-finding methods may include using a camera with a lens
having a narrow depth of field and a calibrated automatic focusing
system. The automatic focus system automatically adjusts the lens
to focus on portions of the object, for example, by maximizing
contrast in resulting images. Then, a range to the object is
determined based on a mechanical position of the calibrated lens.
However, such a calibrated focus technique may not be useful for
objects having minimal optical contrast, or when objects or the
apparatus is in motion. Further, the accuracy of such a system may
be limited by the mechanical tolerances of the calibrated lens.
Another conventional method includes extracting an object distance
from shadows in an image. For example, a conventional shadow method
includes capturing an image of shadows produced when
electromagnetic radiation (e.g., x-ray radiation or light) from an
object is blocked by a mask with a concentric ring pattern such as
a Fresnel Zone Pattern (FZP, a.k.a., Transmission Zone Plate, Zone
Plate, Zone Pattern, Fresnel Zone Plate, etc . . . ) placed between
the object and an image plane.
For the purposes of this application, an FZP may be understood to
be a two-dimensional pattern of alternating light and dark
concentric rings in which a thickness (e.g., radial width) of
successive rings is inversely proportional to the distance from the
center of the rings. For example, the n.sup.th ring of an FZP may
transition (i.e., from dark to light or light to dark) at a radius
r described by the following equation (or by an approximation
thereof): r.sub.n= {square root over (nf.lamda.)} where n is an
integer, .lamda. is the wavelength of the applied light and f is
the focal length of the FZP.
When used with scattered point light sources, such as stars, the
relative positions of the centers of the shadows in the image may
be extracted from the image, and distances to the corresponding
point light sources may be calculated from the shadow center
locations in the image. Such a method is described in L. Mertz and
N. O. Young, "Fresnel transformations of images," in Proceedings of
Conference on Optical Instruments and Techniques, K. J. Habell, ed.
(Chapman and Hall, London 1961) p. 305, incorporated herein by
reference.
However, such conventional shadow ranging methods have a limited
usefulness for when the captured electromagnetic radiation has a
wavelength comparable to the distance between the rings of the FZP,
such as visible light. For example, the visible light may be
diffracted by the edges of rings in the FZP causing shadows in the
image to have poorly defined or smeared edges, thereby making it
difficult or impossible to isolate the centers of resulting shadow
patterns (e.g., see Mertz and Young at FIG. 2).
Conventional scanning holographic methods involve scanning an
object by illuminating a surface of the object with a moving a
pattern of Fresnel Zone Plates (FZPs), serially sensing the
intensity of reflected or transmitted light from the object (i.e.,
a one dimensional intensity signal) as the pattern moves across the
object, and integrating and processing the serially sensed light
intensities to generate three-dimensional information of the
object. In particular, a convolution between the object and the
moving Fresnel Zone Patterns is used to extract three-dimensional
information regarding the object. Conventional scanning holographic
methods are described in Poon T.-C., "Three-dimensional image
processing and optical scanning holography," ADVANCES IN IMAGING
AND ELECTRON PHYSICS 126, 329-350 (2003), and G. Indebetouw, A. El
Maghnouji, R. Foster, "Scanning holographic microscopy with
transverse resolution exceeding the Rayleigh limit and extended
depth of focus," J. Opt. Soc. Am. A 22, 892-898 (2005), each of
which is incorporated herein by reference.
However, conventional scanning holographic methods require that a
pattern be moved across the object while the location of the object
is fixed, thereby limiting the usefulness of the method.
Alternatively, the pattern may be fixed and the object moved across
the pattern, resulting in similar limitations.
In addition, the scanning process may be a relatively slow process
requiring mechanical movements. Thus, scanning is susceptible to
problems produced by mechanical deterioration and inaccuracy, such
as reduced resolution as described above.
Further, since scanning holographic methods serially capture a
one-dimensional light intensity signal from the object and
integrate the serial signal to extract three-dimensional
information, such systems are highly susceptible to variations in
the relative positions of the scanning apparatus and the object
over the duration of the scan. For example, if such a system
captures a first intensity during a first part of the scan, and a
second intensity during a second part of the scan, any variation in
the relative positions of the object and the scanning apparatus (or
even minor changes in the internal arrangement of elements of the
scanning apparatus) may adversely introduce variations into the
captured second intensity, thereby reducing an accuracy, resolution
and usefulness of the system.
In addition, scanning holographic systems are generally large and
complex therefore they may not be suitable for applications
requiring portability or low cost. Further, conventional scanning
holographic systems may require an object to be illuminated by an
interference pattern produced by interfering laser light, may
include a very slow recording process that could take several
minutes or more for each object capture, and the recording process
may disadvantageously require significant mechanical movement of
recording device components and/or the object during the recording
process.
Referring now to the drawings, wherein like reference numerals
designate identical or corresponding parts throughout the several
views.
FIG. 1 is a block diagram of an optical apparatus 100 according to
a first embodiment of the present invention. The optical apparatus
100 is configured to capture a three-dimensional information of an
object 130, and the optical apparatus 100 includes an optical
assembly 110 and an image capture assembly 120. In particular, the
optical assembly 110 receives light from the object 130 along a
receiving optical axis 140. For example, the optical assembly may
receive light from the sun 150 that is reflected or scattered by
reflecting surfaces on the object 130. The received light may be
polychromatic and incoherent light, such as reflected sunlight. In
addition, the light from the object may be fluorescent light or
chemiluminescent light emitted by the object. The optical apparatus
100, in this embodiment, does not illuminate the object but
passively receives light from the object.
The optical assembly 110 transforms the received light according to
a transformation described below, and transmits the transformed
light along the receiving optical axis 140. The image capture
assembly 120 receives the transformed light from the optical
assembly 110, and captures a two-dimensional intensity image of the
transformed light. The captured two-dimensional intensity image
includes geometric information regarding the portions of the object
130 from which light is received at the optical assembly 110. The
geometric information is encoded in the captured two-dimensional
intensity image as a Fresnel hologram. However, such a Fresnel
hologram may be in focus for one cross-section or object focal
plane of the object, while the Fresnel hologram may be out of focus
for other portions of the object that are in front of or behind the
cross-section that is in the object focal plane.
Accordingly, a method for extracting information from the desired
in-focus cross-section may take advantage of differences between
the patterns in that plane and in other planes. Points on the
desired cross-section plane create a composition of Fresnel zone
plates each contributed from an object point on the specific
cross-section plane of the object. Points from other than the
specific cross-section plane contribute noisy patterns that may be
accumulated in the image sensor, and the noisy patterns may be
removed from the image data. For example, using three captured
images, each with different phase factors, a superposition of the
captured images may yield a Fresnel hologram which advantageously
only contains information about a visible portion of the object
that intersects a specific cross-section plane of the object space.
In addition, the present invention also applies to capturing a set
of single object plane holograms, which include a set of
two-dimensional intensity images that encode three-dimensional or
geometric information of an object. The image capture assembly 120
may extract complete three-dimensional information of the object
from the captured set of single object plane holograms. The image
capture assembly may be an opaque light capturing device. An opaque
device is understood to mean a device that is not transparent or
translucent to electromagnetic radiation of relevant frequencies
and intensities, and therefore such a device does not allow such
electromagnetic radiation to pass through.
A hologram is a real positive light intensity distribution that
encodes a complex valued wave-front distribution, including
three-dimensional information regarding the light scattering
surface of the object. Further, in a Fresnel hologram, each point
on the object is encoded into a portion of a sinusoidal Fresnel
zone plate with an entire range of spatial frequency components
present, as noted by Goodman, "Introduction to Fourier Optics," 3rd
Ed., Roberts & Company Publishers, 2005, incorporated herein by
reference. Thus, an image of the object's cross-section may be
recreated optically, by appropriately illuminating a transparency
having the Fresnel hologram, or the image of the object's
cross-section may be recreated by a computer using an electronic
image data of the hologram. The recreated set of images of the
object's cross-section includes three-dimensional information
regarding the shape and distance of an observable surface of the
object.
The optical apparatus 100 may advantageously capture the
three-dimensional object information without moving or being moved
(i.e., the spatial relationship between the optical apparatus 100
and the object 130 may remain unchanged from a time before an image
is captured to a time after the three-dimensional information is
extracted from the captured image by the image capture assembly
120). In addition, the optical apparatus 100 may advantageously
capture the three-dimensional object information while one or both
of the object and the optical apparatus 100 are in motion.
Moreover, the optical apparatus 100 does not project any pattern on
the object, such as is done in a conventional or scanning
holographic method. Further, the optical apparatus 100 does not
include any parts that are required to move while the light is
being received from the object, such as a scanning aperture used in
scanning holography. Thus, without parts that move during image
capture, the optical apparatus 100 may be less expensive to produce
and use, more reliable, quieter, and faster, for example, than an
apparatus used for scanning holography. Further, with respect to
conventional holographic systems that require active illumination
(for example, illumination by a laser), the present invention
advantageously has a simpler design that may be applied to more
types of imaging.
In addition, the present invention does not require an interference
between a light from the illumination (i.e., not scattered by the
object) with a light scattered by the object. Instead, the current
approach diffracts light scattered by the object, which may be
understood as a mutual interference between portions of
electromagnetic radiation wavefronts coming from object itself, and
is not an interference between such scattered light and another
light from the source. Thus; as the mutual interference may be
performed by a few collinear electromagnetic elements (e.g., lenses
and masks, or DOEs, as described below), or even a single
electromagnetic element (e.g., a single DOE, as described below),
the relative differences between optical paths of the interfering
wavefronts are easily controlled (e.g., all the optical paths pass
through the same electromagnetic elements) and therefore,
variations between the lengths of the paths may be more easily
controlled and minimized.
Further, the optical apparatus 100 may advantageously capture the
three-dimensional object information in a single image (e.g., a
single exposure).
Moreover, the optical apparatus 100 may advantageously be able to
capture images with very low levels of light intensity.
Conventional holographic systems may require beam splitters and/or
mirrors that may cause some received light to be lost or wasted. On
the other hand, the optical apparatus 100 does not require the use
of beam splitters or mirrors, and therefore may be able to capture
images with low levels of light intensity.
Further, conventional holographic systems may produce Fourier
holograms in which each object point contributes to interference
fringe patterns that are spread over the entire image plane. Such
conventional systems may require greater light intensity than the
optical apparatus 100, which translates each object point using a
Fresnel Zone Pattern, which may produce fringe patterns for a
particular object point in only a portion of the image plane,
thereby advantageously allowing for lower light intensities.
In addition, the optical apparatus 100 advantageously receives and
transmits light only along a single axis, thereby reducing
susceptibility to axial variation and simplifying the design,
manufacture and use of the optical apparatus 100. Further, the
optical apparatus 100 is coaxial and self-interfering. In
particular, in the present embodiment light from separate light
paths is not interfered to produce an interference pattern or
hologram. Instead, the hologram is produced by diffraction of light
in the optical assembly 110. Although diffraction may be understood
as being produced by interference between each portion of a light
wavefront (i.e., each point along the wavefront being considered a
point source of light according to Huygens wave theory of light),
diffraction produced by a single coaxial assembly, as in the
present embodiment, is much less sensitive to variations in optical
paths between interfering light sources. In particular, light is
self-interfered, according to the present embodiment, because the
only interference is between light waves passing through various
portions of a same optical element (e.g., the optical assembly 110,
or the mask 304 in FIG. 3, described below), and it is much easier
to minimize path length and angle variations for paths passing
through a same optical element, as in the present embodiment, than
it is to control path variations between separate optical paths,
passing through separate optical elements, along separate optical
axes, as in the conventional holography systems. In addition, the
optical apparatus 100 may be used to advantageously capture
polychromatic incoherent light received from the object. Therefore,
a full color three-dimensional image may be recreated from the
hologram recorded by the apparatus.
Although embodiments within this document are described as
transmitting and receiving light, capturing light images and
including optical assemblies, the invention is also applicable to
other types of electromagnetic radiation. Thus, the invention also
includes an electromagnetic radiation apparatus that includes an
electromagnetic radiation assembly that receives a received
electromagnetic radiation from an object.
FIG. 2 is a block diagram that illustrates an example of captured
geometric information according to embodiments of the present
invention. According to the example of FIG. 2, an object 200 is
illuminated by a light source or sources (e.g., the sun 150)
causing light to be scattered or reflected by various light
radiating portions of the object 200. Three example light radiating
portions 206, 208 and 210 scatter light rays 216, 218 and 220,
respectively. These example light rays travel towards the optical
apparatus 100 (shown in FIG. 2 without the detail of FIG. 1). Light
captured by the optical apparatus 100, according to the present
invention, includes geometric information regarding the distance
between the object and the optical apparatus as well as the shape
of observable surfaces of the object 200 from which light is
received at the optical apparatus 100. For example, the captured
light includes information regarding a distance traveled by the ray
of light 218, and in particular, includes the distance between the
light radiating portion 208 and the optical apparatus 100. Further,
the captured light also includes geometric information regarding a
horizontal distance of the light radiating portion 208, for
example, a horizontal distance 212 between an edge of the object
200 and the light radiating portion 208. In addition, the captured
light also includes geometric information regarding a vertical
distance of the light radiating portion 208, for example, a
vertical distance 214 between an edge of the object 200 and the
light radiating portion 208. In this example, horizontal distance
212 and vertical distance 214 are distances measured in a
measurement plane 204 that passes through radiating portion
208.
Thus, an optical apparatus, according to the present embodiment,
may be configured to capture a light including geometric
information regarding each portion of each object from which the
light is received at the optical apparatus. Further, from the
geometric information, the size, shape and location of the visible
portions of each object may be determined. For example, in FIG. 2,
if light is scattered by each external surface of the object 200,
and at least a portion of the scattered light is received at the
optical apparatus 100, then the apparatus 100 may capture light
including geometric information regarding the dimensions (e.g.,
height, width and depth) of each visible surface of the object 200,
as well as information regarding the distance between the object
130 and the front surface of optical apparatus 100.
Although light is scattered by external surfaces in FIG. 2, one of
skill in the art will understand that such an optical apparatus is
also capable of capturing received light from an internal surface
of the object 130 that radiates light to the optical assembly 100
through a translucent or transparent exterior portion of the object
130. In that case, the captured geometric information may include
geometric information regarding an interior portion of the
object.
The optical assembly 110 includes any optical assembly configured
to control a complex amplitude of the transmitted light according
to the complex transformation function described below. Thus, for
example, optical assembly 110 may include one or more refractive
lenses, one or more diffractive optical elements (DOEs), or one or
more spatial light modulators (SLMs).
An incoherent correlator in the regime of diffraction theory may
include every system that produces a pattern of a two-dimensional
Fourier transform of the mask transparency on the system's aperture
at an output plane around a point that is linearly related to an
input point's location, when the incoherent correlator is
illuminated by a single point from some position on the input
plane. Thus, the incoherent correlator produces an output image
including every point in the input plane.
FIG. 3 is a block diagram of an incoherent correlator 300 that may
be used as the optical assembly 110 in the optical apparatus 100
shown in FIG. 1. The incoherent correlator 300 is an optical
assembly that includes a first transforming optical assembly 302, a
mask 304 and a second transforming optical assembly 306. Each of
the first and second transforming optical assemblies 302/306
include the types of converging lenses that would perform a
two-dimensional Fourier transform of received light if they were
illuminated by coherent light (though coherent light is not
required during the operation of the present invention). When the
incoherent correlator 300 is illuminated by a single point light
source 308 from some position on a plane 318, the incoherent
correlator 300 produces a pattern of a Fourier transform of a mask
304 on an output plane 322. The plane 318 is located along and
perpendicular to an optical axis 320 of the incoherent correlator
300, at a distance (z+f.sub.1) from the first transforming optical
assembly 302, where f.sub.1 is a focal length of the first
transforming optical assembly 302 and z is a remaining distance
between the point light source 308 and the first transforming
optical assembly 302. The output plane is located along and
perpendicular to the optical axis 320 at a distance f.sub.2 from
the second transforming optical assembly 306, where f.sub.2 is a
focal length of the second transforming optical assembly 306, in a
direction away from the plane 318. Note that the Fourier transform
of a mask 304 on an output plane 316 is obtained only if z=0. When
z.noteq.0 the optical assembly 300 still performs a correlation
between the object, but with a different function than the Fourier
transform of mask 304. In other words, in the case that z.noteq.0,
the output plane 316 will include an output image that is different
than a Fourier transform of a mask 304.
FIG. 4 is a block diagram of an embodiment of an optical apparatus
400 that includes an optical assembly 300. Optical apparatus 300
includes a first transforming optical assembly 302, a mask 304 and
a second transforming optical assembly 306. Each of the first and
second transforming optical assemblies 302/306 are the types of
optical assemblies (e.g., converging Fourier lenses) that would
perform a two-dimensional Fourier transform operation on a received
coherent light (although the use of the apparatus does not require
coherent light). Light is received from object 130 at the first
transforming optical assembly 302, which transforms the received
light and transmits the transformed light. The mask 304 receives
the transformed light, varies an amplitude and/or phase of the
received coherent transformed light as described below, and
transmits a portion of the received light as the masked light. The
masked light is received by the second transforming optical
assembly 306, which transforms the masked light and transmits a
second transformed light. The image capture assembly 120 receives
and captures the second transformed light, as described above. Note
that when the light received from the object is incoherent, the
transformations performed by the first and second transforming
optical assemblies 302/306 may not be Fourier transformations.
However, the first and second transforming optical assemblies
302/306 are the types of optical assemblies (e.g., converging
Fourier lenses) that would produce a Fourier transform of received
coherent light or received point source light.
The mask 304 includes any device or structure configured to
transform an amplitude and phase of a received light, according to
one or more predetermined complex transmission functions. For
example, the mask 304 may include one or more diffractive optical
elements (DOE), one or more amplitude filters, one or more lenses,
and/or one or more SLMs.
FIG. 5 is a detailed front view of an embodiment of mask 304 that
includes a DOE having an array of plural transform regions 500-514.
Each of the plural transform regions in the diffractive optical
element is configured to transform a phase and/or an amplitude of a
received light according to the transform equations described
below.
The diffractive optical element may include volume-modulated
diffractive optical elements that use a variation in the volume of
refractive material in each transform region to transform the phase
and/or amplitude of the received light and produce transformed
transmitted light. In addition, the diffractive optical element may
include index-modulated diffractive optical elements that use a
variation in a refractive index of refractive material in each
transform region to transform the phase and/or amplitude of the
received light and produce transformed transmitted light. In
addition, the diffractive optical element may include one or more
transmission layers of having a predetermined transmissivity to
thereby vary an amplitude of the received light. Further,
diffractive optical elements that combine one or more features of
volume-modulated, index-modulated and transmission layer
diffractive optical elements may also be included. Methods of
preparing the diffractive optical elements include, for example,
conventional methods such as those described in Salmio et al.,
"Graded-index diffractive structures fabricated by thermal ion
exchange," Applied Optics, Vol. 36, No. 10, 1 Apr. 1997, Carre et
al., "Customization of a self-processing polymer for obtaining
specific diffractive optical elements," Synthetic Metals 127 (2002)
291-294, and Nordman et al., "Diffractive phase elements by
electron-beam exposure of thin As.sub.2S.sub.3 films, Journal of
Applied Physics 80(7), 1 Oct. 1996, each of which is incorporated
herein by reference.
The two-dimensional intensity image captured by the image capture
assembly is generally described by an intensity function o(x,y),
which describes the distribution of light intensities captured at
each point in the image capture plane (i.e., x, y plane). The three
intensity functions o.sub.n(x,y) define the partial contribution to
the overall image intensity contributed by each partial image, and
is related to the overall image intensity function as follows:
.function..times..times..function..times. ##EQU00001##
where B.sub.n is a complex constant.
The transmission functions that produce the three partial images
captured by the image capture assembly 120 are defined as follows:
o.sub.n(x, y)=.intg..intg..intg.s(x', y', z')|h.sub.n(x-x', y-y',
z')|.sup.2dx'dy'dz' (1B) where s(x',y',z') is a function that
describes the intensity at the system input in the vicinity of the
point (x',y',z')=(0,0,0). From the function o(x,y), the geometric
information regarding the light scattering surface (i.e., the
portions of the object facing the optical apparatus 100 that
scatter or emit light that is received at the optical assembly 110)
of the object may be determined in terms of object referenced
coordinates x', y' and z'.
The output response functions of the optical system for a light
point at (x,y,0) are termed point spreading functions (PSF)
h.sub.n(x,y,0). In the present embodiment, h(x,y,0) is a linear
summation of point spreading functions h.sub.1(x,y,0),
h.sub.2(x,y,0) and h.sub.3(x,y,0), which each perform a light
spreading function with respect to the image capture coordinates
(i.e., x, y, 0). PSF h(x,y,0) is defined as follows:
.function..times..times..times..times.I.times..times..pi..times..lamda..t-
imes..times..DELTA..function.I.times..times..theta..times..times.I.times..-
times..pi..times..lamda..times..times..DELTA..times..function.I.times..tim-
es..theta..times..function.I.times..times..phi..function..times..function.
##EQU00002## where .phi..sub.n(x-x.sub.n,y-y.sub.n) are wide-band
random-like phase functions, p.sub.z(x-x.sub.n,y-y.sub.n) are
two-dimensional disk functions centered at points
(x.sub.1,y.sub.1), (x.sub.2,y.sub.2) and (x.sub.3,y.sub.3),
respectively, in the image capture space, i is the imaginary unit
(i.e., i=(-1).sup.0.5), .lamda. is the wavelength of the
propagating light, and .DELTA. is a parameter. Further, the disk
function p.sub.z has a diameter function d(z) that varies the
diameter based on the value of z and thereby limits the diameter of
a corresponding FZP. Further, each PSF is selected to have a
different constant phase value .theta..sub.n.
Although the equation above includes a single value .lamda. for the
wavelength of the propagating light, the above equation may be used
for polychromatic light by assuming that the captured intensity
image is a combination of intensities in plural portions of the
total captured spectrum, and for example, the captured intensity
image may be considered as a combination of captured red light
intensities, captured blue light intensities, and captured green
light intensities. Further, the invention also includes using other
color models to represent the colored image, such as CMYK.
Thus, in the image captured at the image capture device (i.e., at
z=0), the intensity PSFs h.sub.1,2,3 are given by
.function..times..times..times.I.times..times..pi..times..lamda..times..t-
imes..DELTA..times..function.I.times..times..theta..times..times..times..t-
imes.I.times..times..pi..times..lamda..times..times..DELTA..function.I.tim-
es..times..theta..times..function..times. ##EQU00003## Therefore,
the desired light transforming function of each partial function
H.sub.n(u,v) of the optical assembly 110 is the Fourier transform
of h.sub.n(x,y,0) in equation 2 above. Thus, H.sub.n(u,v),
corresponding to embodiments with the spatial multiplexing of
partial mask patterns as shown in Equation 2 and FIGS. 8A-8C, 9A
and 9B.
In alternative time multiplexing embodiments, such as those shown
in FIGS. 14 and 16, H.sub.n(u,v) may be defined as follows:
.function..times..times..function.I.times..times..pi..lamda..times..times-
..DELTA..times.I.times..times..theta..times..function.I.times..times..pi..-
lamda..times..times..DELTA..times.I.times..times..theta..times..function.I-
.times..times..phi..function..times..function..times. ##EQU00004##
where FT represents a Fourier transform operation.
Further, the overall transforming function of the mask H(u,v) is
defined as follows:
.function..times..function. ##EQU00005## where u and v are
coordinates in the plane of the optical assembly 110 corresponding
to the x and y coordinates in the image capture plane (i.e., the u
axis is parallel to the x axis and the v axis is parallel to they
axis).
When the transform regions of a mask include a color filtering
capability configured to filter out or to pass light only centered
at particular frequencies, as described above with respect to FIG.
5. The masks do not have to change when illuminated by various
colors. The response of a mask transparency changes according to
the wavelength of the light, for example as shown in Equation 27
below.
FIG. 6 shows an example of a binary Fresnel Zone Pattern 600, in
which each of zone includes only one of two transmissivity states:
substantially transparent, and substantially opaque, with respect
to the light being transmitted. In this example, the FZP 600 is
printed on a glass substrate 602 that transmits more than 90% of
light within the visual light spectrum using an ink that reflects
or absorbs more than 90% of light within the relevant light
spectrum.
The invention is not limited to binary FZPs having alternating
zones of more than 90% transmission and more than 90%
absorption/reflection, but also includes FZPs having other levels
of transmission, and absorption/reflection, as known in the field
of FZPs. Further, the invention is not limited to FZPs having zones
having a consistent transmissivity throughout each zone (i.e.,
zones that are entirely substantially transparent or entirely
substantially opaque), but also includes FZPs having zones with
varying transmission levels within each zone. In addition, the
invention is not limited only to patterns of complete circular
rings, but also includes patterns of partial rings, such as an
off-axis FZP. Moreover, the invention also includes replacing the
FZP with arbitrary real valued functions which should satisfy
certain conditions to be described below.
FIGS. 7A-7C show examples of sinusoidal FZPs 700, 702 and 704. In
sinusoidal FZPs, transmissivity varies sinusoidally between points
of maximum transmissivity in substantially transmissive zones and
points of minimum transmissivity in less transmissive zones, along
a straight line radiating from the center of the FZP. Further, the
FZPs 700, 702 and 704 each have a different phase.
FIG. 8A-8C show examples of phase functions of Fourier Transformed
FZP patterns with random phase (FT-FZP) 800, 802 and 804 that are
Fourier transforms of FZPs with random phase functions 700, 702 and
704, respectively. Note that the FT-FZP patterns have random-like
pattern. The Fourier transforms of Fresnel zone patterns may be
used to produce the mask functions according to Equation 4
above.
Further, H(u,v) of Equation 4 may be obtained by Fourier transform
of h(x,y,0) from Equation 2.
FIG. 9A is the amplitude portion of a complex transmission function
according to Equation 5, which is a linear combination of three
mask functions each according Equation 4, and corresponding to the
Fourier transform of the three FZPs in FIG. 9C.
FIG. 9B is the phase portion of the complex transmission function
according to Equation 5, which is a linear combination of mask
functions according to Equation 4, and corresponding to the Fourier
transform of the three FZPs with random phase functions in FIG.
9C.
The complex transmission function of Equation 5 and examples
illustrated in FIGS. 9A and 9B may be implemented using a single
DOE or SLM or combinations of DOEs and/or SLMs, as described
above.
Note that the linear combination of FT-FZPs is an amplitude and
phase pattern (e.g., as shown in FIG. 9A-B). The combination of 3
FZPs together is not symmetric in the sense that
h(x,y,0).noteq.h(-x,-y,0). Further, it is well known that a Fourier
transform of non-symmetric functions can not be purely real.
FIG. 9C is an example of the pattern that is generated on the CCD
when a point object is present at the input, as described above
during the process to produce mask patterns shown in FIGS. 9A and
9B.
FIG. 10A is a block diagram of an image capture assembly 1000 that
includes a light intensity capture device 1002 and a capture
control unit 1004. The light intensity capture device 1002 of this
embodiment is a conventional light capturing device, such as a
charge coupled device (CCD) as used in digital cameras, and is
configured to capture a two-dimensional array of light intensity
information (i.e., image of the received light) under the control
of the capture control unit 1004. The invention is not limited only
to CCDs but may also include other devices that capture light
intensity, such as a photographic film or a transparent film, an
X-ray detector, other electromagnetic radiation detectors, a CMOS
device, a diode array, or a photo-detector, etc . . . .
The capture control unit 1004 controls the light capturing
functions of the light intensity capture device 1002 and is
configured to retrieve electronic image data information from the
light intensity capture device 1002. For example, in the present
embodiment, the light intensity capture device includes a CCD
connected to the capture control unit 1004, which is configured,
according to conventional means, to retrieve electronic image data
from the CCD image array. Alternatively, for example, if the light
intensity capture device included a photographic film, the image
capture control unit could include a conventional image scanning
function configured to scan the captured image from the
photographic film, and thereby retrieve the electronic image data.
The invention also includes other conventional methods of capturing
electronic image data, known to those of skill in this field.
The capture control unit 1004 controls the functions of the CCD
1002, and may also include and provide control for conventional
photographic mechanical assemblies such as a shutter and/or a
controllable aperture (not shown) to control aspects of capturing
the image on the CCD 1002. Alternatively, one of skill in the image
capture field will understand that such mechanical assemblies
controlled by the capture control unit 1004 may be arranged in any
convenient location along the light path between the object and the
image capture assembly, or between the light source and the image
capture assembly.
According to the present embodiment, light from a point source is
spread by the pattern in the mask 304 which includes PSFs h.sub.n
(Equation 2) having disk functions p.sub.1(x,y), p.sub.2(x,y) and
p.sub.3(x,y) centered at points (x.sub.1,y.sub.1), (x.sub.2,
y.sub.2) and (x.sub.3, y.sub.3), respectively, in the image capture
space. Thus, an image capture device may be configured to include
three distinct regions within a single light intensity capture
device to receive three distinct partial images produced by mask
304, such as the light intensity capture device 1002 in FIG. 10A.
Further, the image capture device may include three separate light
intensity capture devices to receive the three distinct partial
images produced by mask 304, such as light intensity capture
devices 1006, 1008 and 1010 in the embodiment of image capture
assembly 1012 shown in FIG. 10B.
FIG. 11A is a view of an example of a light intensity capture
device 1100 that includes a charge coupled device 1102 having three
distinct regions 1104, 1106 and 1108. A central location in each
region 1110, 1112 and 1114, respectively, corresponds to a center
of each of the three partial images produced by the optical
assembly 110. In particular, the coordinates of the points 1110,
1112 and 1114 correspond to (x.sub.1,y.sub.1), (x.sub.2, y.sub.2)
and (x.sub.3,y.sub.3), respectively, from Equation 3.
FIG. 11B is an example of a two-dimensional intensity image
according to Equation 1A captured by image capture assembly 120,
including three partial images 1116, 1118 and 1120 produced by
optical assembly 110. Such a two-dimensional intensity image is
converted into a three-dimensional image of the object by the image
capture assembly 120, as described below.
FIGS. 12A-12C show other examples of ways in which the distinct
regions of a light intensity capturing device may be arranged,
where each distinct region includes a center 1200. One of skill in
the art will understand that the light intensity capturing device
may be divided into three or more zones in any convenient manner.
For example, if the light intensity capturing device includes a
randomly addressable CCD, the boundaries of the zones may be
arranged along convenient address regions. Alternatively, if the
light intensity capturing device includes a photographic film, the
boundaries of the zones may be arranged according to the geometries
that are convenient for the dimensions and aspect ratio of the
film.
According to Equation 1A above, an image capture assembly 120
receives and captures light having a light intensity distribution
given by o(x,y). To extract an image of a cross-section of the
object from the captured image, the image capture assembly operates
on the captured image (i.e., intensity function o(x,y)) according
to Equation 1A. Thus, the image of a cross-section of the object
s(x',y',0') is given by the following equation:
.function.''.function..function.I.times..times..pi..lamda..DELTA..times.
##EQU00006## where O.sub.F(x,y) is a linear combination of the
intensity distributions in the partial images as follows:
O.sub.F(x, y)=o.sub.1(x,
y)[exp(-i.theta..sub.3)-exp(-i.theta..sub.2)]+o.sub.2(x,
y)[exp(-.theta..sub.1)-exp(-i.theta..sub.3)]+o.sub.3(x,
y)[exp(-i.theta..sub.2)-exp(-i.theta..sub.1)] (7). The extraction
of the geometric information may be performed using methods from
the field of digital holography, for example as described in I.
Yamaguchi, and T. Zhang, "Phase-shifting digital holography," Opt.
Lett. 22, 1268-1269 (1997), incorporated herein by reference.
In addition, the capture control unit 1004 may include functions
for combining the electronic data for each of the three partial
images according to Equation 7, for extracting the object geometric
information according to Equation 6 and for providing the resulting
object geometric information in a desired format. Alternatively,
those functions may be performed in a general purpose computer
configured to receive the image data from the image capture
assembly.
The object geometric information may be extracted as surface data,
which may be suitable for use in applications such as physical
modeling (e.g., to create a computer model of the object) or
three-dimensional fabrication (e.g., to create a physical
three-dimensional copy of the object) applications. In addition,
the object geometric information may be displayed graphically, for
example using two-dimensional representations of three-dimensional
objects (e.g., a two-dimensional projection such as isometric
projection, or a two-dimensional representation of a
three-dimensional object that may be animated to rotate the object
around one or more axes to better illustrate the three-dimensional
object), or using direct three-dimensional representation of
three-dimensional objects (e.g., holographic display or
projection).
FIG. 13 is a block diagram of an example of a capture control unit
1300 that includes an image data processor 1302 that combines the
electronic image data according to Equation 6 to produce the object
geometric information, and an object data output device 1304 to
output the object geometric information. The image data processor
1302 may be implemented using a conventional processor and
conventional data processing software. The object data output
device 1304 may include any of a number of conventional devices
configured to utilize three-dimensional object geometric data such
as a visual holographic display, a virtual reality environment
display, a three-dimensional object fabrication device (e.g., laser
sintering fabrication device, a digitally controlled lathe, etc . .
. ), a simulation model, a two-dimensional animation of a moving
three-dimensional object, etc . . . . The invention also includes a
capture control unit (not shown) that is configured to include an
interface to an external control device, such as a computer, which
may replace image data processor 1302 and object data output 1304,
to flexibly perform the image data processing functions in a
separate device.
In the embodiments described above, three different mask patterns
having three different transmission functions (e.g., functions
H.sub.1, H.sub.2, and H.sub.3 of equation (4)) are combined in a
single mask, three partial images resulting from the mask patterns
are simultaneously captured, and the three partial images are
combined to obtain geometric object information. However, if the
image capture assembly of FIG. 10A is used, the resulting
resolution of the captured image may be reduced if the pixel array
size is not increased three times so that each of the three images
are the same resolution so that the three partial images may be
captured on a single light intensity capture device. Alternatively,
if the image capture assembly of FIG. 10B is used, or if a single
sensor with three times the area is used, the resulting cost of the
capture apparatus is increased by the cost of two additional light
intensity capture devices or the larger format sensor.
Another embodiment that varies a mask over time may not cause the
possible resolution reduction or cost increase of the preceding
embodiment. In particular, in this embodiment, a mask may be varied
over time, resulting in three different partial images that vary
over time. The three different partial images may be captured by an
image capture assembly configured to capture images over time, and
the three partial images may be combined to extract the geometric
information of the object.
FIG. 14 is a block diagram of an embodiment of an optical apparatus
1400 that varies the mask over time. Optical apparatus 1400 is
similar to the embodiment of the optical apparatus 400 in FIG. 4,
however, the optical apparatus 1400 includes a controllable
incoherent correlator 1402 and a controllable image capture
assembly 1406 that are controlled by a timing controller 1408, and
the optical apparatus 1400 is configured to capture
three-dimensional or geometric information of object 130 using at
least three different images captured at different times.
The controllable incoherent correlator 1402 is similar to the
incoherent correlator 300 of the embodiment shown in FIG. 4.
However, the controllable incoherent correlator 1402 includes a
controllable mask 1404 having a mask that may be controlled by the
timing controller, to controllably transform the amplitude and
phase of light received from the object. One or more spatial light
modulators (SLMs), as described in FIGS. 5, may be used in such a
controllable incoherent correlator.
Further, the controllable image capture assembly 1406 is similar to
the image capture assembly 120 in the embodiment shown in FIG. 4.
However, the controllable image capture assembly 1406 is further
configured to be controlled to capture and retrieve electronic
image data by the timing controller 1408.
FIG. 15 is a block diagram of controllable mask 1404 that includes
a spatial light modulator 1500 under the control of a mask
controller 1502. The mask controller 1502 controls the mask
controller 1502 to transform light according to complex transform
functions H.sub.1, H.sub.2 and H.sub.3 of Equation 4, at times
t.sub.1, t.sub.2 and t.sub.3, as synchronized by the timing
controller 1408. In an alternative embodiment, the mask controller
1502 may be eliminated and the spatial light modulator 1500 may be
controlled directly by the timing controller 1408, or by another
external device not shown (e.g., an external computer operated
controller). Image capture assembly 1406, also under the control of
timing controller 1408 captures three partial images at times
t.sub.1, t.sub.2 and t.sub.3 and combines the partial images to
obtain geometric information for object 130, as described
previously.
FIG. 16 is a block diagram of another embodiment of an optical
apparatus in which the mask is varied over time. In this
embodiment, a mask controller 1600 controls a mechanical position
of a multimask 1612. The multimask 1612 includes three masks 1602,
1608 and 1610 corresponding to the masks H.sub.1, H.sub.2 and
H.sub.3 according to Equation 4. The mask controller moves the
multimask 1612 in directions 1604 to place a corresponding mask
between optical transforming assemblies 302 and 306 at times
t.sub.1, t.sub.2, and t.sub.3, under the control of timing
controller 1408. Image capture assembly 1406, also under the
control of timing controller 1408 captures three partial images at
times t.sub.1, t.sub.2 and t.sub.3 and combines the partial images
to obtain geometric object information for object 130, as described
previously. The multimask 1612 may include masks in a linear
arrangement as shown in FIG. 16, or may include masks arranged in a
radial arrangement, or any other suitable arrangement.
The three partial images may also be produced and captured
simultaneously using an arrangement including three different
optical assemblies having different masks and arranged to each
receive a portion of the light received from the object.
FIG. 17 is a block diagram of an embodiment of an optical apparatus
1700 having optical assemblies 1702, 1704 and 1706 that are
configured to each receive a portion of the received light from the
object by an arrangement of partially transmissive and reflective
mirrors 1708, 1710 and 1712 (e.g., "partially-silvered" mirrors).
An image capture assembly 120, such as the embodiments shown in
FIGS. 10A and 10B, captures and processes the received partial
images as described above.
Although the embodiments are described using only transmissive
optical elements (e.g., refractive lenses and transmissive masks)
one of skill in the art will understand that the invention also
includes alternative embodiments in which one or more of the
optical elements may be replace with a corresponding reflective
optical element, as desired.
FIG. 18 is an embodiment of an optical apparatus 1800 that is
similar to optical apparatus 400 shown in FIG. 4. However, optical
apparatus 1800 includes a reflective mask 1802 that is configured
to reflect unmasked light, instead of transmitting the unmasked
light as in mask 304. A beam splitter 1804 redirects the light
reflected by mask 1802 to the second transforming optical assembly
306.
Other arrangements of mirrors or beam splitters to conveniently
direct light are also included in the present invention.
In the optical apparatus embodiments described above, when the
electromagnetic radiation received from the object includes a wide
bandwidth, it is possible to capture frequency information in the
image capture assembly. Thus, it is possible for the image capture
assembly to determine a corresponding electromagnetic radiation
frequency or frequencies for each portion of the object. For
example, when a white light is received at the optical assembly
from the object, the image capture assembly may determine the color
of each portion of the object from the image captured by the image
capture assembly.
In addition, it may be possible to increase the resolution of the
captured three-dimensional information by reducing the bandwidth of
the received light. For example, the resolution of the captured
three-dimensional information may be increased by limiting the
bandwidth of the received light to those frequencies of light close
to the color red. Such an increase in resolution may be obtained by
filtering received or transmitted light in the optical assembly to
have a reduced bandwidth using conventional filters, or by
irradiating the object with a reduced bandwidth light source, using
methods known by those of skill in the art.
However, images captured using a reduced light bandwidth may not
include a sufficient level of information regarding the various
colors of the received light, and therefore may not allow for the
image capture assembly to determine colors of the object to a
sufficiently high level of accuracy. Accordingly, other embodiments
of the invention may include plural channels each configured to
receive light and capture images within different portions of the
electromagnetic spectrum, and them to combine the separately
captured images to produce full spectrum three-dimensional
information regarding the object.
FIG. 19 is a block diagram of optical apparatus 1900 that receives
light from object 130. The received light is partitioned into three
light portions 1903, 1905 and 1907 by light partitioning devices
1902, 1904 and 1906, respectively. The three light portions 1903,
1905 and 1907 each include a subset of the bandwidth of the
received light. For example, light portion 1903 may include only
light frequencies near the color red, light portion 1905 may
include only light frequencies near the color green and light
portion 1907 may include only light frequencies near the color
blue. The light partitioning devices 1902, 1904 and 1906 may
include any combination of dichroic mirrors, color filters, mirrors
or other partially transmissive frequency filtering devices known
to those of skill in the art.
The light portions 1903, 1905 and 1907 are received by optical
assemblies 1908, 1910 and 1912, respectively, which each may be
configured to transform the received light as described above. That
is, each of the optical assemblies 1908, 1910 and 1912 may
transform a light portion of the received light as described above
(e.g., using three partial mask patterns or a time varying
pattern), and transmit the transformed light to an image capture
assembly 1012 that includes a separate light capture assembly for
each of the three partial mask patterns, or to an image capture
assembly 1000 (not shown) that includes a single light capture
assembly configured to capture different images over time or
different partial images within different regions of the
assembly.
In addition, the optical apparatus 1900 includes an image combining
apparatus 1913 configured to receive image data representing the
images captured at image capture assemblies 1012 and combine the
image data to produce combined broadband three-dimensional
information regarding the object. For example, the optical
apparatus 1900 may be able to capture full-color three-dimensional
information with a higher resolution than the embodiments described
above.
Although the embodiments of FIG. 19 include received light that is
separated into three portions, other embodiments in which light is
separated into other numbers of portions are also included.
An incoherent correlator may equivalently be implemented with
alternate optical apparatuses other than the lens/mask/lens
arrangements described above. For example, by applying the
well-known thin lens approximation for lenses, the incoherent
correlator may be implemented with a single optical transforming
element and a single mask, with either the mask or the optical
transforming element arranged to first receive light from the
object. In addition, the optical assembly 110 may be implemented
using a single diffractive optical element. The equations 1-5 above
therefore also apply to embodiments having a single transforming
optical assembly and a mask, and embodiments having an optical
assembly implemented using only a single diffractive optical
element.
FIG. 20A is a block diagram of an example of an optical apparatus
2000 that is similar to the optical apparatus 400 shown in FIG. 4.
However, the optical apparatus 2000 does not require a second
transforming optical element. Instead light is received from the
object 130 by optical transforming element 2002, which transforms
the received light and transmits the transformed light. The
transformed light is received by mask 2004 which selectively
transmits a portion of the transformed light. Image capture
assembly 120 receives and captures an image of the selectively
transmitted light and obtains geometric information regarding
object 130 from the captured image, as described above.
FIG. 20B shows an example of an optical apparatus 2006 that is
similar to the optical apparatus 400 shown in FIG. 4. However, the
optical apparatus 2006 does not require a first transforming
optical element. Instead light is received from the object 130 by
mask 2008 which selectively transmits a portion of the received
light. The second optical transforming element 2010 receives the
selectively transmitted light, transforms the received light and
transmits the transformed light. Image capture assembly 120
receives and captures an image of the transformed light and obtains
geometric information regarding object 130 from the captured image,
as described above.
There may be a relatively high cost to manufacture optical
assemblies having a conventional incoherent correlator structure.
An alternative embodiment of the present invention the optical
assembly may be implemented using a single diffractive optical
element (DOE) in place of the incoherent correlator.
A single DOE may replace the incoherent correlator (e.g.,
incoherent correlator 300 including first and second transforming
optical assemblies 302/306 and mask 304 in the embodiment shown in
FIG. 4) described above. A DOE that is equivalent to the incoherent
correlator is the product of the mask filter function and the
transmission functions of the first and second transforming optical
assemblies, H.sub.DOE, defined as follows:
.function..function.I.times..times..times..pi..lamda..times..times..times-
..times..intg..intg..function..times..function.I.times..times..times..pi..-
lamda..times..times..times..times.d.times.d ##EQU00007## where f is
the focal length of the first and second transforming optical
assemblies included in the DOE, h(x,y,0) is given above in Equation
2, and other parameters are as described with respect to Equation
4.
Further, the focal lengths of the lenses are not required to be the
same. When the focal lengths are different, the H.sub.DOE, is
defined as follows:
.function..function.I.pi..function..lamda..times..times..times..times..ti-
mes..intg..intg..function..times..function.I.pi..lamda..times..times..time-
s..times.d.times.d ##EQU00008## Note that although Equations 8 and
9 do not include literal P function terms, p.sub.o(x,y) is part of
h(x,y,0), and when the integral in Equations 8 and 9 are solved,
the convolution with P(u,v) is obtained.
FIG. 20C is a block diagram of an example of an optical apparatus
2012 that is similar to the optical apparatus 400 shown in FIG. 4.
However, the optical apparatus 2012 does not require first and
second transforming optical elements. Instead light is received
from the object 130 by mask 2014 which transmits light based on a
complex transformation of the received light. Mask 2014 may be
implemented using only a single diffractive optical element, as
described above. Image capture assembly 120 receives and captures
an image of the transformed light and obtains geometric information
regarding object 130 from the captured image, as described
above.
FIG. 21 is a block diagram of an embodiment of optical apparatus
100 in which the optical element 110 includes a reflective type
diffractive optical element, for example, such as the diffractive
optical elements shown in FIG. 5. In this embodiment, the optical
apparatus 100 receives a light from object 130 along a receiving
optical axis 2104. The optical apparatus 100 transforms and
reflects the received light to produce a transmitted light
transmitted back along optical axis 2102. The transmitted light is
reflected by a beam splitter 2100 to an image capture assembly 120
located along a capturing optical axis 2102 of the optical
apparatus. In the present embodiment, capturing optical axis 2102
is arranged at an angle of approximately 90 degrees from the
receiving optical axis 2104. However, other angles between the
receiving and capturing optical axes are also included in the
invention.
With only two optical axes, the current embodiment may
advantageously reduce a size of the optical assembly 100, while
exhibiting less sensitivity to axial variations than in
conventional holography systems.
An objective-side optical assembly, such as an objective lens, a
zoom lens, a macro lens, a microscope, a telescope, a prism, a
filter, a monochromatic filter, a dichroic filter, a complex
objective lens, a wide-angle lens, a camera, a pin-hole, a light
slit, a mirror, or any other optical assembly may be placed between
the optical assembly and the object to collimate, focus, invert or
otherwise modify the light from the object, prior to the light
being received at the optical assembly. Such an arrangement may
advantageously allow light from objects or portions of objects to
be received, when it would not be possible or practical to receive
that light without the inclusion of the objective-side optical
assembly.
Further, an objective-side optical assembly may include refractive
or diffractive optical elements configured to at least partially
cancel any disadvantageous wavelength dispersal effects that may be
caused by the optical apparatus 100, as described by Goodman,
"Introduction to Fourier Optics," 3rd Ed., Roberts & Company
Publishers, 2005, at p. 212, incorporated herein by reference.
FIG. 22A shows an alternative embodiment including the features of
the embodiment in FIG. 1, as well as an objective-side optical
assembly 2200 that receives light from the object and transmits a
received light to the optical assembly 110. The objective-side
optical assembly 2200 in the present embodiment includes a
magnifying refracting objective lens that produces a magnified
image of the object 130 centered on an image plane 2202. Thus, the
present embodiment may capture more detailed geometric information
regarding a magnified portion of the object.
The present invention may also operate in conjunction with an
existing sensor-less camera, which is understood herein to be any
camera from which the existing digital light sensor (e.g., CMOS
device or CCD) or light sensitive capture medium (e.g., film and
film transport mechanism) has been removed, or moved away from the
image plane of the camera to allow an apparatus according to the
present invention to be used with the remaining optical and
mechanical components of the camera. For example, film, film
transport mechanisms and the rear cover of an existing 35 mm film
camera may be removed and replaced with an optical assembly and
image capture device according to the present invention, thereby
making the existing camera capable of capturing three-dimensional
information. Such an arrangement advantageously allows the present
invention to conveniently take advantage of and operate with
existing photographic lenses, shutter systems and aperture control
systems of existing cameras.
FIG. 22B shows an example of an embodiment of an optical apparatus
2204 including features similar to the optical apparatus 100 shown
in FIG. 1. In addition, the optical apparatus 2204 is configured to
operate with an existing sensor-less camera 2206, which receives
light from the object 130 along an optical axis 140, and
manipulates the light using conventional camera features (e.g.,
lens, ground glass focusing screen, shutter and aperture of the
existing camera) to produce an image of the object centered at
image plane 2208. The optical apparatus 2204 includes a chassis
having mechanical and electrical attachment features suitable for
coupling the optical apparatus 2204 to a portion of the existing
sensor-less camera 2206 near the image plane produced by the optics
of the existing sensor-less camera 2206 (e.g., as a replaceable "3D
back" of the camera). The optical assembly 110 receives light from
the image of the object at the image plane 2208 and transmits a
transformed light, which may be received, captured and processed to
extract three-dimensional information of an object by the image
capture assembly 120, as described above.
The present invention may also operate in conjunction with an
existing camera. In particular, the optical assembly in the
embodiment described herein may be used in conjunction with a
conventional digital or film camera to illuminate the image plane
of the conventional camera with a Fresnel hologram or partial
Fresnel holograms of the observed object. The conventional camera
may be used to capture an image of the hologram fringe patterns
using the corresponding conventional means (e.g., light sensitive
film or digital sensor), and image data corresponding to the fringe
patterns may be converted into three-dimensional data of the object
using a general purpose computer.
The invention is not limited to a single DOE that includes a
transmission function based on a linear combination of three
transmission functions each having a Fourier transforms of a FZP.
On the other hand, the invention also includes receiving a portion
of the light from the object at each of three DOEs, which produce
three partial images that are combined.
FIG. 23 shows a block diagram of an embodiment of an optical
apparatus 2300 including partially reflective and transmissive
mirrors 1708, 1710 and 1712 that direct a light received from
object 130 to each of three diffractive optical elements 2302, 2304
and 2306, respectively, which each perform a transforming function
including a Fourier transform of a FZP. The image capture assembly
2308 extracts three-dimensional information from an image of the
light transmitted by the diffractive optical elements, similar to
the manner described above.
In addition, alternative embodiments of the optical assembly 110
may consist of a single SLM as shown in FIG. 5 or one or more
SLMs.
Further, the invention is not restricted only to using three mask
patterns to produce three partial hologram images that are
combined. The invention also includes using an off-axis holographic
method that employs a single off-axis hologram instead of three
masks.
During reconstruction of an image from an off axis hologram each
term is diffracted toward a different direction and therefore a
desired angular separation can be achieved even from a single
hologram, by taking advantage of the fact that angular separation
in diffraction theory is directly translated to a spatial frequency
separation. This characteristic may be exploited based on the idea
that, when performing a convolution between functions f and g, it
is equivalent to transform f and g to the frequency domain by a
Fourier transform to obtain functions F and G, obtain a product of
F and G, and transform the product back by an inverse Fourier
transform. Thus, an optical apparatus that shifts a spatial
frequency spectrum of a received light may be advantageously used
to create a Fresnel hologram.
An optical apparatus that produces an off-axis Fresnel Zone Pattern
(OAFZP) in response to point input light source can be used to
convolve a received light rather than the FZPs in the embodiments
above, and convolution using the OAFZP based assembly will allow
for a convenient separation of terms in the frequency domain.
FIG. 24 shows an example of an OAFZP 2400.
To synthesize the off-axis FZP we may introduce a linear phase term
to the equation for the on-axis FZPs described above, to result in
the following OAFZP transformation function
.function..function..times..times..function.I.times..times..pi..function.-
.times..lamda..times..times..DELTA.I.times..times..times..pi..function..al-
pha..times..times..beta..times..times..lamda..times..function.I.times..tim-
es..pi..function..times..lamda..times..times..DELTA.I.times..times..times.-
.pi..function..alpha..times..times..beta..times..times..lamda..times..func-
tion.I.times..times..phi..function. ##EQU00009##
FIG. 25 is a block diagram of a portion of an optical apparatus
including a composite mask 2520. Light 2518 is received and
refracted by DOE 2514 towards lens 2502 having focal length f 2512.
Waves produced by mask 2520 and lens 2502, respectively, interfere
with each other to produce OAFZP 2508 at image plane 2510.
Therefore, a composite mask that produces a single off-axis FZP may
replace the masks or diffractive optical elements, based on Fourier
transforms of FZPs, in any of the optical apparatuses described
above.
A filter that creates a Fresnel hologram that includes object space
information for only the observable portion of the 3D scene that
intersects with a single transverse plane is one that produces an
output having an amplitude PSF with a magnitude in the form of a
FZP and a phase with a random, wide-band nature. According to
Equation (4) the amplitude PSF h(x,y,0) of an optical correlator is
the inverse Fourier transform of the filter function H(u,v). A
filter H(u,v) may be synthesized such that its inverse Fourier
transform is the amplitude PSF h(x, y, 0)=|h(x, y, 0)|exp[i.phi.(x,
y, 0)] (11)
The magnitude of h(x,y,0) is a FZP of the form,
.function..times..times..function..times..function..times..function.I.tim-
es..times..pi..lamda..DELTA..times.I.times..times..theta..function.I.times-
..times..pi..lamda..DELTA..times.I.times..times..theta.
##EQU00010##
where p.sub.z(x,y)=1 in some given disk area S and p.sub.z(x,y)=0
outside the area S. The intensity PSF in this case is
.function..function..times..function.I.pi..lamda..DELTA..times.I.times..t-
imes..theta..function.I.times..times..pi..lamda..DELTA..times.I.times..tim-
es..theta. ##EQU00011## According to equation (3), such an
intensity PSF guarantees that the intensity distribution on the
correlator output plane is an on-axis Fresnel hologram of at least
one single transverse plane, the input plane of the correlator.
When H(u,v) is a wide-band, random-like function satisfying
equation (12), the h(x,y,z) resulting from equation (11) includes
speckle noise in each and every plane besides the plane z=0. As
mentioned above, on the plane z=0 the PSF's magnitude |h(x,y,0)| is
a FZP because this is the constraint defined in equation (12) for
which H(u,v) is synthesized.
The process of reconstructing the cross-section of the input plane
by a computer is identical to the process described by equation
(7). To get rid of the bias term (the 0.sup.th order) and the twin
image, at least three such holograms may be recorded with different
phase values and the image can be obtained by a superposition
according to equation (7).
When amplitude PSF has random, wide-band phase distribution
.phi.(x,y), any object point located at any transverse plane that
is at least a Rayleigh distance (i.e., 0.61.lamda./NA, where NA
means numerical aperture) away from the input plane generates a
meaningless noisy pattern on the output plane. The contribution of
this noisy pattern to the recorded hologram in the output plane has
a similar fate as of the DC term in the conventional digital
hologram. Thus, this noise may be almost completely removed by the
superposition of the three holograms described by equation (7). The
remaining noise portion on the final hologram after the
superposition induces a relatively weak noisy background in the
reconstructed image.
In order to section the object into different cross-sections, the
filter function may be constrained such that the magnitude of its
inverse Fourier transform will satisfy equation (12). In other
words, this magnitude may be in the form of a FZP. However, this
FZP should be obtained only on the output plane. At any plane
before or behind, at least a Rayleigh distance from the output
plane, the obtained pattern should preferably resemble a noisy
speckle pattern. Such a goal may be achieved if the phase of
h(x,y,0) has a random wideband nature, which may be caused by
starting the computing process with a random phase function filter,
and forcing a second constraint on filter function H(u,v). The
second constraint results from the requirement that the filter is
preferably a phase-only function, and may achieve two goals: first,
in order to get maximum transmission efficiency, the system's
filter should preferably not absorb any light that passes through
the correlator.
Second, in order to get an amplitude PSF with a wide-band phase
distribution, the filter should preferably have unit transmission.
However, it should be noted that the second constraint is not
crucial for proper operation, and these preferences may be relaxed,
while still achieving the claimed benefits. A different constraint
can be chosen, or even only the main constraint at the PSF space
mentioned above can be enforced without using any second constraint
at all. Preferably, the optimal filter function simultaneously
satisfies as much as possible of both constraints. One possible way
to select the filter function is by an iterative algorithm such as
POCS (Projection Onto Constraints Sets), which is known by the
following other names: Gershberg-Saxton, Ping-Pong, or IFTA
(Iterative Fourier Transform Algorithm). Alternatively, other
similar algorithms may be used. An example of selecting the filter
function according to the POCS algorithm is shown in the flow
diagram of FIG. 26.
The method of FIG. 26 begins with the selection of a random
phase-only filter in S2600, such as
H.sub.st(u,v)=exp[i.phi..sub.R(u,v)]. This filter is inversely
Fourier transformed to the PSF space, in S2602, and the obtained
function is projected onto the constraint set such that the
magnitude of the function h(x, y) is a FZP function of the form of
equation (12), in S2604. The phase of the function h(x, y) remains
unaffected by this step. Following this projection, the new PSF is
Fourier transformed back to the filter space, in S2606. The new PSF
is projected from the filter space onto the constraint set of the
Fourier space, in S2608, where the magnitude of the function H(u,v)
is replaced by the unity magnitude, and the phase function remains
unaffected. These steps are repeated until the obtained filter is
close enough to meeting both the constraint sets, as determined by
the user's requirements.
In the description above, it is assumed that in order to
reconstruct a specific cross-section of an object, the intensity
PSF should be in the form of a FZP like that described by Equation
(12). However, as described below, there are many other possible
functions which can be used to successfully reconstruct a
cross-section of an object. These functions should satisfy certain
conditions which are discussed in the following. Using different
intensity PSFs can reduce the number of holograms to be captured
and superposed to fewer than the three holograms described above in
the case of an intensity PSF of the form of Equation (13). In this
example, the reduced number of holograms are still on-axis,
providing all the advantages of on-axis holograms described above.
Note that when using functions other than FZPs as the intensity
PSF, the recorded holograms may no longer be considered as Fresnel
holograms.
For example, the cross-section may be constructed based on
capturing two on-axis holograms. The corresponding two amplitude
PSFs are |w.sub.1(x,y)|exp[i.phi..sub.1(x,y)] and
|w.sub.2(x,y)|exp[i.phi..sub.2(x,y)], where .phi..sub.1(x,y) and
.phi..sub.2(x,y) are random wide-band functions. w.sub.1(x,y) and
w.sub.2(x,y) are arbitrary functions which satisfy certain
constraints, explicitly presented in the following. The two
captured holograms are, H.sub.1(x, y)=I(x, y)*|w.sub.1(x, y)|.sup.2
H.sub.2(x, y)=I(x, y)*|w.sub.2(x, y)|.sup.2 (14) where I(x,y) is
the intensity distribution of a single object's cross-section
located at the input plane.
The two captured holograms are subtracted one from the other such
that the final hologram is H(x, y)=I(x, y)*[|w.sub.1(x,
y)|.sup.2-|w.sub.2(x, y)|.sup.2] (15)
The magnitudes of the two amplitude PSFs are constrained such that
the Fourier transform of the function
w(x,y)=|w.sub.1(x,y)|.sup.2-|w.sub.2(x,y)|.sup.2 should be a phase
only function. Such a constraint allows the reconstruction of an
object's cross section to advantageously be performed by finding
two magnitude functions w.sub.1(x,y) and w.sub.2(x,y) that satisfy
the constraint that the function w(x,y) is real valued, on one
hand, and on the other hand the constraint that the Fourier
transform of this function w(x,y) is purely phase function.
First, a real random function is selected, for example using a
computer to select the function. Next, the function is Fourier
transformed and the magnitude of the transformed function is
replaced by the unity function. Finally, the phase-only spectrum is
inversely Fourier transformed back to the image plane. This short
procedure guarantees that, on one hand, the resulting function is
real valued, because the Fourier transform of the resulting
function remains an odd function. On the other hand the Fourier
transform of w(x,y) is constrained to be a phase-only function.
Once functions w.sub.1(x,y) and w.sub.2(x,y) are selected to
satisfy FT[w(x, y)]=exp[i.psi.(u, v)] the object's cross-section
may be reconstructed by Fourier transforming the final hologram
given in equation (14) and multiplying the result of the Fourier
transformation by the transform by exp[-i.psi.(u, v)], which has
known characteristics. Therefore, the reconstructed cross section
of the object may be obtained by multiplying the Fourier transform
of the recorded hologram by the complex conjugate of exp[i.psi.(u,
v)], as shown in the following:
.times..times..function..times..function.I.times..times..psi..function..t-
imes..times..function..function..function..times..function.I.times..times.-
.psi..function..times..times..function..times..times..function..times..fun-
ction.I.psi..function..times..times..function..times..function.I.psi..func-
tion..times..function.I.psi..function..times..times..function..function.
##EQU00012##
Thus, in summary, the filter may be synthesized as follows. First,
two Fourier related functions are selected as described above, such
that one is a bipolar real function in the object domain
w(x,y)=|w.sub.1(x,y)|.sup.2-|w.sub.2(x,y)|.sup.2 and the other is
exp[i.psi.(u,v)] in the frequency domain. Next, the positive part
of w(x,y), designated as w.sub.P(x,y), is separated from the
negative part, designated as w.sub.N(x,y), where w.sub.N(x,y) is a
positive function. The amplitudes of the two PSFs are given by:
w.sub.1(x,y)= {square root over (w.sub.p(x,y))} and w.sub.2(x,y)=
{square root over (w.sub.N(x,y))}. The phase of these PSFs is
calculated by two separated POCS algorithms, for example as shown
in FIG. 26. Further, the magnitude in the PSF domain is enforced to
be |w.sub.1(x,y)| in one POCS and |w.sub.2(x,y)| in the other POCS,
and not FZPs as suggested before.
In each of the POCS algorithms, the frequency domain may be
constrained to get a phase-only function in order to achieve
maximum transmission efficiency for the filters. In the image
domain, the amplitude functions may be constrained to obtain
w.sub.1(x,y) in one POCS and w2(x,y) in the other POCS. Starting
these POCS algorithms from a random phase distribution in the
frequency domain allows the phase functions of the two amplitude
PSFs to be random-like wide-band functions.
Finally, the filter-finder POCS algorithms yield two phase only
filters F.sub.1(u,v)=exp[i.theta..sub.1(u,v)] and
F.sub.2(u,v)=exp[i.theta..sub.2(u,v)] having inverse Fourier
transforms |w.sub.1(x,y)|exp[i.phi..sub.1(x,y)] and
|w.sub.2(x,y)|exp[i.phi..sub.2(x,y)], respectively. Functions
w.sub.1(x,y) and w.sub.2(x,y) are computed such that the Fourier
transform of |w.sub.1(x,y)|.sup.2-|w.sub.2(x,y)|.sub.2 is again the
phase only function exp[i.psi.(u,v)].
In the following example, the image of the cross-section of the
object is reconstructed using only a single on-axis hologram. In
this example, the single amplitude PSF is denoted by
|s(x,y)|exp[i.phi.(x,y), where .phi.(x,y) has a random wide-band
nature. The single captured hologram is, H(x, y)=I(x, y)*|s(x,
y)|.sup.2 (17)
where I(x,y) is the intensity distribution of the object's
cross-section located at the input plane. Unfortunately, the
Fourier transform of the function |s(x,y)|.sup.2 is not a pure
phase only function because, for such positive-only functions, the
high bias term yields a large magnitude value in the origin of the
spectral plane at (u,v)=(0,0), significantly larger than the rest
of the spectrum values. Therefore, a positive-only function may not
be transformed to a phase-only spectral function in which the
spectral magnitude is one everywhere. The constraint on the
magnitude of the amplitude PSFs that can be imposed is that the
Fourier transform of the bipolar function s'(x, y)=|s(x,
y)|.sup.2-[.intg..intg..sub.A|s(x, y)|.sup.2dxdy-1]/A should be a
phase only function, where A is the area of the image plane. As
described below, this kind of constraint enables object
cross-section reconstruction using a direct calculation to find a
magnitude function satisfying, on one hand the constraint that the
function s'(x,y) is real valued, and on the other hand the
constraint that the Fourier transform of this function is purely a
phase function. A real random bipolar function, for example,
selected by a computer, is Fourier transformed and the magnitude of
the transformed function is replaced by the unity function. Next,
this phase-only spectrum is inversely Fourier transformed back to
the image plane. The obtained bipolar function is converted to a
positive function by adding the constant value equal to the
absolute value of the function's minimal value. This short
procedure guarantees that, on one hand, the resulting function is
real valued because its Fourier transform remains an odd function.
On the other hand, during the procedure we enforce the condition
that the Fourier transform of a resulting function is a phase-only
function. After selecting a function s(x,y) that satisfies the
condition FT{|s(x,y)|.sup.2-[.intg..intg..sub.A|s(x,
y)|.sup.2dxdy-1]/A}=exp[i.psi.(u, v)] (18)
the object's cross-section can be reconstructed by Fourier
transforming the final hologram given in equation (17), introducing
a zero value at the origin of the spectral plane and multiplying
the transform by exp[-i.psi.(u, v)]. Therefore, the reconstructed
cross section of the object is approximately given by,
FT.sup.-1{{FT{H(x, y)}[1-.delta.(u, v)]+.delta.(u,
v)}exp[-i.psi.(u, v)]} FT.sup.-1{{FT{I(x, y)*|s(x,
y)|.sup.2}[1-.delta.(u, v)]+.delta.(u, v)}exp[-i.psi.(u, v)]}
FT.sup.-1{{FT{I(x, y)}FT{|s(x, y)|.sup.2}[1-.delta.(u, v)]+67 (u,
v)}exp[-i.psi.(u, v)]} FT.sup.-1{FT{I(x, y)}exp[i.psi.(u,
v)]exp[-i.psi.(u, v)]}.apprxeq.I(x, y) (19) where .delta.(u,v)=1
for (u,v)=(0,0) and .delta.(u,v)=0 for all points other than
(u,v)=(0,0). The entire process of filter synthesizing includes now
a single POCS algorithm.
In summary, reconstructing the cross-section of the object using a
single on-axis hologram may be performed as follows. First, two
Fourier related functions are selected as described above, where
one function is a bipolar real unbiased function in the object
domain s'(x,y) and the other in the frequency domain is
exp[i.psi.(u,v)]. Next s'(x,y) is converted to a positive function
by adding the constant value |min{s'(x,y)}| to s'(x,y). The
amplitude of the PSF is now s(x, y)= {square root over (s'(x,
y)+|min{s'(x, y)}|)}{square root over (s'(x, y)+|min{s'(x, y)}|)}.
The phase of this PSF is calculated by a POCS algorithm. The
frequency domain is constrained to get a phase-only function to
obtain maximum transmission efficiency for the filter. The image
domain is constrained to get the amplitude function s(x,y).
Starting a POCS algorithm with a random phase distribution in the
frequency domain allows the phase of the amplitude PSF to be a
random-like wide-band function. The POCS algorithm yields a
phase-only filter F(u,v)=exp[i.theta.(u,v)] having an inverse
Fourier transform equal to |s(x,y)|exp[i.phi.(x,y)]. The function
s(x,y) is computed such that the Fourier transform of the bipolar
real function |s(x, y)|.sup.2-[.intg..intg..sub.A|s(x, y)|.sup.2
dxdy-1]/A is the phase only function exp[i.psi.(u,v)]. Following is
a description of alternative methods to capture sets of sectioning
holograms for reconstructing images of different cross-sections of
a 3D scene. Each alternative method has different advantages.
FIG. 27A is a schematic and block diagram of a first embodiment of
an apparatus configured to capture different cross sections of an
object 130. In this embodiment, an optical apparatus 1400, such as
the optical apparatus shown in FIG. 14, may be configured to
capture plural holograms corresponding to different positions of
object 130. In this example, object 130 may be moved along axis
2708 by a mechanical device, such as a movable platform 2702,
connected by gear 2704 to motor 2706. Further, although not shown,
the position of the platform 2702 may be controlled by computer
1408, or the position may be independent of computer 1408. By
shifting the input object plane along axis 2708, as shown in FIG.
27A, each of the plural different captured holograms may be used to
obtain a corresponding cross-section of the object 130.
FIG. 27B is a schematic and block diagram of a second embodiment of
an apparatus configured to capture different cross sections of an
object 130, in which the position of the object 130 may remain
unchanged, while the position of the optical apparatus 1400,
mounted on a movable platform 2710, is varied along the axis 2708.
FIG. 27C is a schematic and block diagram of a third embodiment of
an apparatus configured to capture different cross sections of an
object 130. In this option, a location of an input plane may be
varied between 2714 and 2716 by mechanically moving a location of
lens 302, using for example, a platform 2712 by a gear 2704 and a
motor 2706. In addition, other methods of changing a focal or
object input plane known to those in the field of optics are also
included in the present invention.
FIG. 27D is a block diagram of a fourth embodiment of an apparatus
configured to capture different cross sections of an object 130,
without moving either the object 130 or the apparatus 1400. In this
embodiment, the effective focal length of the correlator's input
lens 302 is varied using an electrically controlled diffractive
lens (ECDL) 2718, which may be implemented using a SLM.
Alternatively, lens 302 may be replaced by the ECDL 2718. In this
embodiment, holograms may be captured using various focal lengths
of the correlator's input lens or ECDL, with each hologram
corresponding to a different cross-section.
Although different cross-sections may be obtained by changing the
input plane of the object or the input focal plane, different
cross-sections may alternatively be obtained by changing a location
of the output plane.
FIG. 28A is a schematic and block diagram of a fifth embodiment of
an apparatus configured to capture different cross sections of an
object 130, by moving a location of image capture assembly 1406
with respect to incoherent correlator 1402. In this example, a
motor 2806 controls a movable platform 2802, using gear 2804. The
platform 2802 is configured to move image capture assembly 1406
along axis 2808. Plural holograms corresponding to plural
cross-sections may be obtained at each different position of image
capture assembly 1406 along axis 2808.
FIG. 28B is a schematic and block diagram of a sixth embodiment of
an apparatus configured to capture different cross sections of an
object 130, by moving object 130 and image correlator 1402, each
attached to movable platform 2810, with respect to image capture
assembly 1406.
FIG. 28C is a schematic and block diagram of a seventh embodiment
of an apparatus configured to capture different cross sections of
an object 130, by moving a location of an output lens 306, and
thereby changing the cross-section captured by the image capture
assembly 1406. FIG. 28D is a block diagram of a eighth embodiment
of an apparatus configured to capture different cross sections of
an object 130, by varying an effective focal length of lens 306
using ECDL 2814, as described above.
Instead of changing or moving the correlator or some of its
components, holograms may be captured while varying the filter
function such that each varied filter satisfies the two constraint
sets described above, for each different desired transverse plane
in the observed scene. Thus, by varying the filters, cross-sections
for the entire observed 3D space may be obtained.
For example, using the embodiment shown in FIG. 16, the filters in
each of masks 1602, 1608, and 1610 may be selected to correspond to
three different desired cross-sections of object 130.
In the embodiments described above, the process of capturing the
plural cross-sections of the observed 3D space is performed
serially, plane by plane, which may require an unacceptable amount
of time. However, all the transverse planes may be captured at once
by splitting the output plane into several channels corresponding
to the number of cross-sections desired to be recorded in
parallel.
FIG. 29 is a block diagram of a ninth embodiment of an apparatus
configured to capture different cross sections of an object 130, by
capturing plural partial images simultaneously. In this embodiment,
filter 1404 includes a combination of four different filter
functions each corresponding to a different portion of the optical
spectrum and each observing a different cross-section of object
130. Light from correlator 1402 is received by light partitioning
devices 2910, 2912, 2914, and 2916, which are each configured to
reflect one portion of the light, corresponding to one of the
filter functions, to a corresponding image capture assembly 2902,
2904, 2906, or 2908, respectively. The light partitioning devices
2910, 2912, 2914, and 2916 may include any combination of dichroic
mirrors, color filters, mirrors or other partially transmissive
frequency filtering devices known to those of skill in the art.
Alternatively, light partitioning devices 2910, 2912, 2914, and
2916 may be configured to reflect a portion of the entire spectrum
of light, and the filter 1404 may be selected such that the
relative length of light paths to each of image capture assemblies
2902, 2904, 2906, and 2908, correspond to different cross-sections
of the object 130.
In the embodiment shown in FIG. 29, each image capture assembly
receives only a portion the output light intensity. However, the
present invention also includes using several correlators in
parallel to obtain several cross-sections of the scene.
FIG. 30A is an example of an embodiment in which each correlator
can be implemented by two microlenses, which are contained in
double lens arrays as is shown in FIG. 30B. In this setup the
efficiency is not compromised but the field of view may be
reduced.
FIG. 30C shows an example including parallel correlators using
double convex microlens arrays. This arrangement enables using more
correlators in the process compared to the setup with double planar
microlens arrays. However, with these convex arrays one may need to
use many digital cameras distributed on a wide surface of a sphere
around the object. In order to avoid this last constraint, one can
use a DOE with or without one or more spherical lenses, for example
as shown in FIG. 30D, which all together operate as the multiplexed
array of correlators in a similar manner like the double convex
microlens arrays.
One of skill in the art will understand that the optical
apparatuses described above are not limited to capturing only
reflected sunlight, but may also determine the shape and distance
of object portions that do not reflect light but instead emit a
fluorescent light, a black body radiation, a chemiluminescent light
or other light produced by the object, or objects that reflect or
scatter light from sources other than the sun. In addition, an
optical apparatus, according to the present embodiment, is not
limited to capturing only the external shape and distance of
objects, but may also capture information regarding internal
portions of an object that radiate (i.e., reflect or fluoresce)
light from an internal portion through a transparent or translucent
surface of the object to the optical apparatus.
The present invention is also not limited to capturing geometric
information regarding an object using a Cartesian coordinate system
(e.g., x, y, z), but also includes capturing geometric information
using any other coordinate system that may fully describe the
shape, size and location of the object, such as a three-dimensional
polar coordinate system (e.g., .phi., .theta., r), an earth
referenced coordinate system such as the global coordinate system
(e.g., latitude, longitude, elevation), a coordinate system
incorporating an ellipsoid earth model reference system such as
WGS-84, an earth centered earth fixed Cartesian coordinate system
(ECEF) (e.g., x, y, z), Universal Transverse Mercator (UTM),
Military Grid Reference System (MGRS), or World Geographic
Reference System (GEOREF), etc . . . . Further, although Cartesian
type measurement terms such as "vertical," "horizontal" and "range"
are used throughout the present description, those terms are
intended to also include corresponding measurement terms in other
reference systems, but which are omitted from the description
herein for reasons of clarity and brevity.
Advantages of the present invention may make embodiments of the
invention suitable for three-dimensional imaging applications that
are impossible or impractical without the present invention. For
example, the present invention may be applied to capturing
three-dimensional movies/video/television images, performing
three-dimensional object recognition for moving objects or
stationary objects from a moving or stationary platform (e.g.,
military targeting applications, robotic sensing applications,
autonomous aid to vision impaired users, etc . . . ), autonomous
navigation and safety functions (e.g., automatically guide an
automobile to stay on a road and avoid collisions with moving and
stationary objects), weather sensing (e.g., capture
three-dimensional information regarding clouds or air masses
detected with radar, visible light, or infrared and/or ultraviolet
light, etc . . . ), security functions (e.g., monitor locations and
identity objects in a room, monitor identities and locations of
people in a building, three-dimensional synthetic radar, etc . . .
), and three-dimensional environmental mapping for virtual reality
simulation (e.g., create three-dimensional model of tourist
destination for virtual visit), or three-dimensional models of
environments that are difficult or impossible to observe directly
(e.g., internal body cavities, microscopic environments, hazardous
environments, extraterrestrial environments, underground or sea
environments, remote environments, etc . . . ).
Although examples described above deal with optical components and
visible light, the present invention also applies to receiving
other forms of electromagnetic radiation from an object and
determining three-dimensional information of the object based on
the received electromagnetic radiation, such as x-ray radiation,
microwave radiation, radio frequency radiation, and ultraviolet and
infrared light. For example, embodiments of the invention described
above may be modified to replace optical components (e.g., lenses,
mirrors, diffractive optical elements, SLMs) with corresponding
x-ray components, such as are known in the art and as described in
i) U.S. Pat. No. 6,385,291 to Takami, ii) Pereira et al., "Lithium
x-ray refractive lenses," Proc. SPIE 4502, 173 (2001)., and iii)
Beguiristain et al., "Compound x-ray refractive lenses made of
polyimide," Proc. SPIE, vol. 4144, pp. 155-164, each of which is
incorporated herein by reference.
Further, for example, the present invention may be applicable as a
replacement for existing x-ray imaging systems (e.g., CT scanners).
As the present approach does not require any moving parts, x-ray
imaging done using an embodiment of the present invention
advantageously may produce a scan more reliably, with higher
resolution, greater speed and less total radiation exposure to the
patient.
Each of the embodiments described above may be modified to replace
optical elements with equivalent x-ray elements known to those of
skill in the art to produce three-dimensional information based on
a received x-ray radiation from an object (i.e., a
three-dimensional x-ray image). For example, the present invention
may be applicable as a replacement for existing electron microscope
technology.
Further the invention also applies to other forms of propagating
energy waves, such as sound waves and may be applied to produce
three-dimension object information using passive or active
sonar.
Coherent light, which propagates according to the paraxial
approximation, is described mathematically as a convolution between
an input aperture and a quadratic phase function with an
appropriate parameter in a denominator of an exponent power
indicating a propagation distance of the wave from the input
aperture. Thus, the complex amplitude (i.e., the electrical field)
distribution O(x,y) on some transversal plane, in a distance z from
the input plane, may be given (in the Fresnel approximation) by
.function..intg..intg..function.''.times..times.I.times..times..pi..lamda-
..times..times..function.''.times.d'.times.d' ##EQU00013##
where S(x', y') is the complex amplitude on the input aperture at
the transverse plane z=0, .lamda.is the wavelength of the
propagating light and (x', y'), (x,y) are the coordinates of the
input and output planes, respectively. For 3D objects,
contributions from the object points are accumulated to the
following expression,
.function..intg..intg..intg..function.'''.times..times.I.times..times..pi-
..lamda..times.'.function.''.times.d'.times.d'.times.d'
##EQU00014##
where (x',y'z') are the coordinates of the input space. In a
conventional holography approach that produces a Fresnel hologram,
the complex amplitude O.sub.z(x,y) may be interfered with a
reference beam and the intensity of the resulting interference
pattern is recorded on a photographic plate or a digital camera.
However, according to the present invention, a convolution similar
to Equation 21 may be performed differently using incoherent light,
because the Fresnel propagation described in Equation 20 may be
valid only for coherent illumination.
For a two-dimensional (2D) input intensity function s(x,y) and an
intensity point spread function (PSF) |h(x,y)|.sup.2, a correlator
output intensity (e.g., of a correlator such as shown in FIG. 3)
distribution may be given by the following convolution, o(x,
y)=s(x, y)*|h(x, y)|.sup.2=.intg..intg.s(x', y')|h(x-x',
y-y')|.sup.2dx'dy' (22)
where the asterisk denotes a 2D convolution, h(x,y) is the
amplitude PSF in the system, but under coherent illumination.
h(x,y) is related to the 2D inverse Fourier transform of the filter
function H(u, v) (304 in FIG. 3), as the following,
.function..intg..intg..function..times..function.I.times..times..pi..lamd-
a..times..times..times..times..times..times..times..times.d.times.d
##EQU00015##
where f.sub.2 is the focal length of the second lens in the
correlator shown in FIG. 3. To solve for 3D objects rather 2D, a
response of the incoherent correlator to a 3D input function may be
determined. Further, although the input function is
three-dimensional, the output and the convolution remain
two-dimensional. In fact the correlator response for a 3D input is,
o(x, y)=.intg.s(x, y, z)*|h(x, y,
z)|.sup.2dz=.intg..intg..intg.s(x', y', z')|h(x-x', y-y',
z')|.sup.2dx'dy'dz' (24)
To calculate the general 3D amplitude PSF h(x,y,z) of the system, a
response to a single point located at some point (x,y,z) in the
vicinity of the rear focal point of the correlator may be
determined. Such a calculation produces the 3D PSF of the system
which may be used to calculate the system response to any possible
3D input. Since the system is known as space invariant it is
correct to calculate the system response to a point on the optical
axis at some point (0,0,-z), and to generalize the response toward
a general location at (x,y,z). The input point is located a
distance f.sub.1+z from the lens 302 at the point 308 (i.e.,
0,0,-z), as shown in FIG. 3.
The Fresnel integrals in Equations 20 and 21 can be used to
calculate the light distribution because a single monochromatic
point source is by definition a spatial coherent source. By
substituting the representation of a single point source,
represented by a delta function .delta.(0,0,-z), into Equation 21
as the input S(x,y,z), the result on the plane of the first lens
302 is a diverging quadratic phase function as follows,
.function..intg..intg..intg..delta..function.'''.times..function.I.pi..la-
mda..function.'.times.''.times.d'.times.d'.times.d'.function.I.pi..lamda..-
function..times. ##EQU00016##
where f.sub.1 is the focal length of the first lens in the
correlator shown in FIG. 3. This quadratic phase function is known
as the paraxial approximation of the spherical wave propagating in
the z direction, and the paraxial approximation of a concave
spherical lens transparency. This spherical wave propagates through
the incoherent correlator and beyond the correlator the beam
becomes a converging spherical wave. It may be shown that at the
plane where the beam is focused one gets the Fourier transform of
the transparency function of the mask H(u, v). This Fourier
transform is scaled according to the specific location of the focal
plane and is multiplied by a quadratic phase function.
Assuming that the three optical thin elements L.sub.1, L.sub.2 and
H(u,v) of the incoherent correlator (e.g., elements 302, 306 and
304, respectively, in FIG. 3) are all located at the same plane,
the diverging spherical wave and the two adjunct lenses L.sub.1 and
L.sub.2 can be replaced by a single equivalent lens having a focal
length f.sub.e, as follows:
.times..function..function. ##EQU00017##
In a system having the equivalent lens in place of the correlator,
once the system is illuminated by a plane wave, the complex
amplitude on a back focal plane of equivalent lens L.sub.e is
related to the 2D Fourier transform of the transparency function
H(u,v). This means that the complex amplitude on the back focal
plane, at a distance f.sub.e from the equivalent lens L.sub.e
is
.function..times..times..function.I.pi..lamda..times..times..function..ti-
mes..times..intg..intg..function..times..function.I.times..times..pi..lamd-
a..times..times..function..times..times..times..times..times..times.d.time-
s.d ##EQU00018##
Note that the incoherent system is analyzed above according to the
rules of coherent diffraction theory because the beams are
considered to have been emitted from a single infinitesimal point.
Since the output of the system is located a distance f.sub.2 from
the equivalent lens L.sub.e, the output complex amplitude is
obtained after a free propagation beyond the back focal plane of
the equivalent lens L.sub.e.
Free propagation of coherent light may be obtained, as mentioned
above in Equation 20, as the result of convolution between the
complex amplitude in the starting plane and a quadratic phase
function. According to this, the output complex amplitude is,
.times..function..function.I.pi..lamda..function..function..times..times.-
.function.I.pi..lamda..times..times..function..times..times..intg..intg..f-
unction..times..function.I.times..times..times..pi..lamda..times..times..f-
unction..times..times.d.times.d.function.I.pi..lamda..function..function..-
times. ##EQU00019##
Note that although the function in Equation 28 deals with three
dimensions, the convolution is always in 2D. Equation 28 expresses
the general 3D amplitude Point Spreading Function (PSF) of the
system when it is illuminated by coherent light. Further, Equation
28 can be simplified by writing explicitly the convolution
integral, switching the order of integration and using the
well-known result of the Fourier transform of quadratic phase
function. Such a simplification reduces the four integrals of
Equation 28 to a double integral as follows:
.function..function.I.pi..lamda..times..times..times..times..intg..intg..-
function..times..function.I.pi..function..function..lamda..times..times..t-
imes..function..times..times..function.I.times..times..pi..lamda..times..t-
imes..times..times..times..times..times..times.d.times.d
##EQU00020##
Another equation used to synthesize the filter in the system is the
expression of the amplitude PSF for any point at the plane z=0,
given by substituting f.sub.e(0)=f.sub.2 in Equation 29, as
follows,
.function..function.I.pi..lamda..times..times..times..times..intg..intg..-
function..times..function.I.times..times..times..pi..lamda..times..times..-
times..times..times..times..times..times.d.times.d ##EQU00021##
As described above, the intensity PSF for incoherent systems and
for intensity distributions on the input and output planes is
|h(x,y,z)|.sup.2. The intensity PSF represents the impulse response
of general incoherent systems. By taking the absolute square of
Equation 29 one finds that the 3D intensity PSF is,
.function..times..intg..intg..function..times..function.I.pi..function..f-
unction..lamda..times..times..times..function..times..times..function.I.ti-
mes..times..times..pi..lamda..times..times..times..times..times..times..ti-
mes..times.d.times.d ##EQU00022##
The general expression of Equation 31 can be used to compute the
PSF for a given filter or the required filter for a given PSF.
According to Equation 26 the expression in the exponent of Equation
31 is,
.function..times..function..times..function..function..times..function..f-
unction..function. ##EQU00023##
Substituting Equation 32 into Equation 31 yields
.function..intg..intg..function..times..function.I.times..times..pi..time-
s..times..lamda..times..times..function..times..times..function.I.pi..lamd-
a..times..times..times..times..times..times..times..times.d.times.d
##EQU00024##
The general expression of Equation 33 can be used to compute the
PSF for a given filter or the required filter for a given PSF.
To obtain a Fresnel hologram, which is a convolution between any
object and a quadratic phase function, an incoherent intensity PSF
in a shape of a quadratic phase function with a number of cycles
(Fresnel number) dependent on the distance z is selected. This may
not be achieved directly because |h(x,y,z)|.sup.2 is a positive
real function while a quadratic phase function has negative and
imaginary values.
One method of selecting such a PSF is to compose the PSF
|h(x,y,z)|.sup.2 as a sum of three terms, one of them is the
required quadratic phase function, and their sum maintains the
condition that |h(x,y,z)|.sup.2 is a positive real function. Thus,
a PSF such as shown in Equation 34
.function..function..times..times..function.I.pi..lamda..times..times..DE-
LTA..function..times..times..function.I.pi..lamda..DELTA..function..times.
##EQU00025##
satisfies this condition, where .DELTA.(z) is a parameter linearly
related to the distance z and p.sub.z(x,y) is a disk function with
the diameter d(z), different for different values of z, that
indicates the limiting aperture of a corresponding Fresnel Zone
Pattern (FZP). The amplitude PSF for this choice is
.function..times..function..times..function.I.pi..lamda..DELTA..function.-
.times..times..times..function..times..function.I.pi..times..lamda..DELTA.-
.function..times..times..function..times..times..function.I.pi..function..-
times..lamda..DELTA..function..times..function.I.pi..function..times..lamd-
a..DELTA..function. ##EQU00026##
Note that a possible arbitrary pure phase term can multiply
h(x,y,z) without affecting the square magnitude of h(x,y,z) given
in Equation 34. However in order to get a Fresnel hologram of all
the object's points, it is preferred that h(x,y,z) remains as a sum
of two quadratic phase terms along the propagation axis. Of the
possible phase functions that can multiply h(x,y,z), only a
quadratic phase function may satisfy the condition that h(x,y,z) is
a sum of two quadratic phase terms after propagating a distance.
Accordingly, it is appropriate to assume that h(x,y,z) is a sum of
two quadratic waves with the same magnitude of Fresnel number but
with opposite signs, as given in Equation 35. Further, as described
below, two quadratic waves with different Fresnel numbers may be
used in an optimized solution.
Based on the desired h(x,y,z), H(u,v) may be calculated by
inversing Equation 30, to produce the following filter function in
Equation 36.
.function..intg..intg..function..times..function.I.times..times..pi..lamd-
a..times..times..times..times..function.I.times..times..times..pi..lamda..-
times..times..times..times.d.times.d ##EQU00027##
Substituting Equation 35 into Equation 36 yields Equation 37
.function..times..function.I.times..times..pi..lamda..times..times..gamma-
..times..times..function.I.times..times..pi..lamda..times..times..gamma..t-
imes..function. ##EQU00028##
where P(u,v) is the Fourier transform of p.sub.o(x,y). Note that
H(u,v) is 2D function which determines the dependency of h(x,y,z)
along the transverse coordinates (x,y). The dependency of h(x,y,z)
along the z axis is dictated by the location of input source
point.
The intensity PSF may be obtained by substituting the filter
function of Equation 37 into Equation 31. Assuming that the filter
function is
.function..times..function.I.times..times..pi..lamda..times..times..gamma-
..times..times..function.I.times..times..pi..lamda..times..times..gamma..t-
imes..function. ##EQU00029##
therefore, Equation 31 becomes,
.function..intg..intg..times..function.I.times..times..pi..lamda..times..-
times..gamma..times..times..function.I.times..times..pi..lamda..times..tim-
es..gamma..times..function..times..times..times..function.I.times..times..-
pi..lamda..times..function..times..times..function.I.times..times..times..-
pi..lamda..times..times..times..times.d.times.d ##EQU00030##
After summation corresponding terms, the result is,
.function..intg..intg..times..times..function.I.times..times..pi..functio-
n..times..gamma..times..times..times..lamda..times..times..gamma..times..t-
imes..function..times..function.I.times..times..pi..function..times..gamma-
..times..times..times..lamda..times..times..gamma..times..times..function.-
.times..times..function..times..function.I.times..times..times..pi..lamda.-
.times..times..times..times.d.times.d ##EQU00031##
Calculating the Fourier transform,
.function..times..function.I.times..times..pi..gamma..times..times..funct-
ion..times..lamda..times..times..function..times..gamma..times..gamma..tim-
es..times..times..times..times..function.I.times..times..pi..times..times.-
.gamma..times..times..function..times..lamda..times..times..function..time-
s..gamma..times..gamma..times..times..times..function.
##EQU00032##
Calculating the square magnitude yields,
.function..times..function.I.times..times..times..pi..times..times..gamma-
..times..times..function..times..lamda..times..times..function..function..-
gamma..times..times..function.I.times..times..times..pi..times..times..gam-
ma..times..times..function..times..lamda..times..times..function..function-
..gamma..times. ##EQU00033##
The parameter .DELTA.(z) is,
.DELTA..function..function..gamma..times..times..times..gamma..times..tim-
es..function..times. ##EQU00034##
Equation 43 gives the value of A(z), the distance of a
reconstructed image point as a function of the object point's
location on the z axis, for the general choice of
y.sub.1,2=.+-.y.
Equation 34 describes the intensity PSF captured by an image
capture device according to the present invention. This PSF has
three additive terms that are all concentrated in the center of the
image capture plane. Therefore, convolution of the object function
with such an intensity PSF yields three overlapped non-separated
terms. However, it is desired to extract only a desired convolution
term between the object and a single quadratic phase function among
the three convolutions with three terms of the intensity PSF. A
desired convolution between the object and a single quadratic phase
function among the three convolutions with three terms of Equation
34 may be extracted using methods similar to those in digital
holography, for example as described by I. Yamaguchi, and T. Zhang,
"Phase-shifting digital holography," Opt. Lett. 22, 1268-1269
(1997), which is incorporated herein by reference.
The correlator may perform three operations of convolution between
the object and three PSFs equipped with three different constant
phase values. These PSFs may be synthesized by introducing three
filter masks with three different constant phase values as
follows,
.function..times..function.I.times..times..pi..lamda..times..times..gamma-
..times.I.times..times..theta..times..times..function.I.times..times..pi..-
lamda..gamma..times.I.times..times..theta..function.
##EQU00035##
By the relation of Equation 33, it can be shown that the three
filters induce three intensity PSFs as follows,
.function..function..times..times..function.I.times..times..pi..lamda..ti-
mes..times..DELTA..times..times..times.I.times..times..theta..times..funct-
ion.I.times..times..pi..lamda..times..times..DELTA..times..times..times.I.-
times..times..theta. ##EQU00036##
Substituting the three PSFs of Equation 45 into Equation 24 yields
the output intensity images that may be recorded by a camera or
other suitable image capture device (e.g., CCD, CMOS, photographic
film, etc . . . ):
.function..times..intg..function..function..times.d.times..intg..function-
..function..times.d.times..times..function.I.times..times..theta..times..i-
ntg..function..times..function..times..function.I.times..times..pi..lamda.-
.times..times..DELTA..times..times..times..times.d.times..times..function.-
I.times..times..theta..times..intg..function..function..times..function.I.-
times..times..pi..lamda..DELTA..times..times..times..times.d
##EQU00037##
From these three images, a single term of convolution between the
object s(x,y) and one of the quadratic phases may be extracted. A
possible formula to isolate such a single convolution is O.sub.F(x,
y)=o.sub.1(x,
y)[exp(-i.theta..sub.3)-exp(-i.theta..sub.2)]+o.sub.2(x, y)[exp
(-i.theta..sub.1)-exp(-i.theta..sub.3)]+o.sub.3(x,
y)[exp(-i.theta..sub.2)-exp(-i.theta..sub.1)] (47)
O.sub.F(x,y) is a final complex valued hologram which sat
.function..intg..function..function..times..function.I.times..times..pi..-
lamda..times..times..DELTA..times..times..times..times.d
##EQU00038##
The function O.sub.F(x,y) is the final hologram which contains
information on the one 3D image only. Such an image s(x,y,z) can be
reconstructed from O.sub.F(x,y) by calculating the inverse
operation to Equation 48, as follows,
.function..function..function.I.times..times..pi..lamda..times..times..DE-
LTA..function..times. ##EQU00039##
Subsequently, the process of obtaining a single hologram with good
separation between the three terms will be described. However,
practical aspects of performing the convolution with three
different PSFs are described first. There are several ways in which
the filters may be multiplexed to produce the three partial images.
For example, a time multiplexing system, such as the embodiment
shown in FIG. 14, multiplexes the filters over time. Alternatively,
the multiplexing may be done in the output plane of a single
channel, for example as in the embodiment shown in FIG. 4. When a
single point source is introduced at the point (0,0,0) the system's
PSF is a pattern of 3 FZP with 3 different phases, distributed at 3
separated locations on the output plane. This 2D amplitude PSF is
given by,
.function..times..times..times.I.times..times..pi..times..lamda..DELTA..f-
unction..function.I.times..times..theta..times..times.I.times..times..pi..-
times..lamda..DELTA..function..function.I.times..times..theta..times..func-
tion. ##EQU00040##
where (x.sub.n,y.sub.n) is the center point of the nth FZP.
h(x,y,0) of Equation 50 may be used to synthesize the filter H(u,v)
by Fourier transform of h(x,y,0). For synthesizing the diffractive
optical element (DOE) in a lensless system, for example the
embodiment shown in FIGS. 1 and 20C, one may multiply the filter
function by the transmission function of the two spherical lenses,
to identify the overall transmission function of the DOE as
follows,
.function..function.I.times..times..pi..function..lamda..times..times..ti-
mes..times..times..intg..intg..function..times..function.I.times..times..p-
i..lamda..times..times..times..times..function.I.times..times..times..pi..-
lamda..times..times..times..times.d.times.d ##EQU00041##
where h(x,y,0) is given in Equation 50.
So far we have dealt with holograms of 3D scenes. Holograms when
viewed by humans create an authentic illusion of viewing a
realistic 3D scene. However, reconstructing the same hologram by a
computer creates a virtual 3D space in which it may be difficult to
determine where the image is in-focus, and what is the exact
distance of each object from the camera. The hologram by its nature
is only a 2D matrix and as so it may not adequately represent all
the information contained in the 3D scene.
To overcome this drawback we suggest here a new design for the
spatial filter of the same incoherent correlator described before.
With the new filter the correlator can function as an image
sectioning system that can image every transverse section of the 3D
space separately. Instead of including information regarding the
entire 3D scene, a hologram recorded according to this embodiment
contains only the information regarding one single transverse
cross-section of the 3D scene, and excludes information regarding
other transverse planes. In order to image the entire 3D scene, one
may record plural single cross-section holograms for different
transverse cross-sections of the 3D scene. A method of capturing
plural single cross-section holograms, each including information
regarding a single cross-section of a 3D scene, and combining the
information together to obtain complete 3D information regarding
the 3D scene may be referred to as Sectioning Holographic Imaging
(SHI). In the above described embodiment we propose several
possible setups aimed to capture multiple holograms of the entire
3D space, cross-section by cross-section. Some of these setups
capture the holograms by multiple shots, and others even suggest
doing it by a single snap shot.
Numerous modifications and variations of the present invention are
possible in light of the above teachings. It is therefore to be
understood that within the scope of the appended claims, the
invention may be practiced otherwise than as specifically described
herein.
* * * * *